## 2016 |

Benini, Anna Miriam A note on repelling periodic points for meromorphic functions with bounded set of singular values Journal Article Revista Matemática Iberoamericana, 32 (1), pp. 265 - 272, 2016. @article{Benini2016, title = {A note on repelling periodic points for meromorphic functions with bounded set of singular values}, author = {Anna Miriam Benini}, url = {http://arxiv.org/abs/1411.6796}, year = {2016}, date = {2016-02-01}, journal = {Revista Matemática Iberoamericana}, volume = {32}, number = {1}, pages = {265 - 272}, abstract = {Let $f$ be a meromorphic function with bounded set of singular values and for which infinity is a logarithmic singularity. Then we show that $f$ has infinitely many repelling periodic points for any minimal period $ngeq 1$, using a much simpler argument than the more general results for arbitrary entire transcendental functions}, keywords = {}, pubstate = {published}, tppubtype = {article} } Let $f$ be a meromorphic function with bounded set of singular values and for which infinity is a logarithmic singularity. Then we show that $f$ has infinitely many repelling periodic points for any minimal period $ngeq 1$, using a much simpler argument than the more general results for arbitrary entire transcendental functions |

Lenci, Marco A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point Journal Article Chaos, Solitons & Fractals, 82 , pp. 148 - 154, 2016. @article{Lenci2016-1, title = {A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point}, author = {Marco Lenci }, url = {http://arxiv.org/abs/1511.05906}, doi = {10.1016/j.chaos.2015.11.024}, year = {2016}, date = {2016-01-01}, journal = {Chaos, Solitons & Fractals}, volume = {82}, pages = {148 - 154}, abstract = {Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0, 1], with countably many surjective branches and a strongly neutral fixed point in 0.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0, 1], with countably many surjective branches and a strongly neutral fixed point in 0. |

Levitin, Michael; Seri, Marcello Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential Journal Article Operators and Matrices, 10 (1), pp. 223 - 245, 2016. @article{Levitin2016, title = {Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential}, author = {Michael Levitin and Marcello Seri}, url = {http://arxiv.org/abs/1503.08615}, year = {2016}, date = {2016-01-01}, journal = {Operators and Matrices}, volume = {10}, number = {1}, pages = {223 - 245}, keywords = {}, pubstate = {published}, tppubtype = {article} } |

Marò, Stefano; Sorrentino, Alfonso Aubry-Mather theory for conformally symplectic systems Unpublished 2016. @unpublished{MaroSorrentino2016, title = {Aubry-Mather theory for conformally symplectic systems}, author = {Stefano Marò and Alfonso Sorrentino}, url = {http://arxiv.org/abs/1607.02943}, year = {2016}, date = {2016-07-12}, abstract = {In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system. |

Paci, Giulia; Cristadoro, Giampaolo; Monti, Barbara; Lenci, Marco; Degli_Esposti, Mirko; Castellani, Gastone C; Remondini, Daniel Characterization of DNA methylation as a function of biological complexity via dinucleotide inter-distances Journal Article Philosophical Transactions of the Royal Society A, 2016 , pp. 20150227, 2016. @article{Paci2016, title = {Characterization of DNA methylation as a function of biological complexity via dinucleotide inter-distances}, author = {Giulia Paci and Giampaolo Cristadoro and Barbara Monti and Marco Lenci and Mirko Degli_Esposti and Gastone C. Castellani and Daniel Remondini}, url = {http://arxiv.org/abs/1511.08445}, doi = {10.1098/rsta.2015.0227 }, year = {2016}, date = {2016-02-08}, journal = {Philosophical Transactions of the Royal Society A}, volume = {2016}, pages = {20150227}, abstract = {We perform a statistical study of the distances between successive occurrences of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the CG dinucleotide distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g. fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between CG dinucleotides provides useful insights into characterizing and classifying organisms in terms of methylation functionalities.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We perform a statistical study of the distances between successive occurrences of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the CG dinucleotide distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g. fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between CG dinucleotides provides useful insights into characterizing and classifying organisms in terms of methylation functionalities. |

Knight, Georgie; Munday, Sara Escape rate scaling in infinite measure preserving systems Journal Article Journal of Physics A: Mathematical and Theoretical, 49 (8), pp. 085101, 2016. @article{Knight2016, title = {Escape rate scaling in infinite measure preserving systems }, author = {Georgie Knight and Sara Munday}, url = {http://iopscience.iop.org/article/10.1088/1751-8113/49/8/085101?fromSearchPage=true}, doi = {10.1088/1751-8113/49/8/085101}, year = {2016}, date = {2016-01-20}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {49}, number = {8}, pages = {085101}, abstract = {We investigate the scaling of the escape rate from piecewise linear dynamical systems displaying intermittency due to the presence of an indifferent fixed point. Strong intermittent behaviour in the dynamics can result in the system preserving an infinite measure. We define a neighbourhood of the indifferent fixed point to be a hole through which points escape and investigate the scaling of the rate of this escape as the length of the hole decreases, both in the finite measure preserving case and infinite measure preserving case. In the infinite measure preserving systems we observe logarithmic corrections to and polynomial scaling of the escape rate with hole length. Finally we conjecture a relationship between the wandering rate and the observed scaling of the escape rate.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We investigate the scaling of the escape rate from piecewise linear dynamical systems displaying intermittency due to the presence of an indifferent fixed point. Strong intermittent behaviour in the dynamics can result in the system preserving an infinite measure. We define a neighbourhood of the indifferent fixed point to be a hole through which points escape and investigate the scaling of the rate of this escape as the length of the hole decreases, both in the finite measure preserving case and infinite measure preserving case. In the infinite measure preserving systems we observe logarithmic corrections to and polynomial scaling of the escape rate with hole length. Finally we conjecture a relationship between the wandering rate and the observed scaling of the escape rate. |

Bonanno, Claudio; Chouari, Imen Escape rates for the Farey map with approximated holes Journal Article International Journal of Bifurcation and Chaos, to appear , 2016. @article{Bonanno2016, title = {Escape rates for the Farey map with approximated holes}, author = {Claudio Bonanno and Imen Chouari}, url = {http://arxiv.org/abs/1512.04432}, year = {2016}, date = {2016-10-01}, journal = {International Journal of Bifurcation and Chaos}, volume = {to appear}, abstract = {We study the escape rate for the Farey map, an infinite measure preserving system, with a hole including the indifferent fixed point. Due to the ergodic properties of the map, the standard theoretical approaches to this problem cannot be applied. To overcome this difficulties we propose here to consider approximations of the hole by means of real analytic functions. We introduce a particular family of approximations and study numerically the behavior of the escape rate for "shrinking" approximated holes. The results suggest that the scaling of the escape rate depends on the chosen approximation, but "converges" to the behavior found for piecewise linear approximations of the map in \cite{KM}.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study the escape rate for the Farey map, an infinite measure preserving system, with a hole including the indifferent fixed point. Due to the ergodic properties of the map, the standard theoretical approaches to this problem cannot be applied. To overcome this difficulties we propose here to consider approximations of the hole by means of real analytic functions. We introduce a particular family of approximations and study numerically the behavior of the escape rate for "shrinking" approximated holes. The results suggest that the scaling of the escape rate depends on the chosen approximation, but "converges" to the behavior found for piecewise linear approximations of the map in cite{KM}. |

Sorrentino, Alfonso Homogenization of the Hamilton-Jacobi equation Unpublished 2016. @unpublished{SorrentinoHomog2016, title = {Homogenization of the Hamilton-Jacobi equation}, author = {Alfonso Sorrentino}, url = {http://www.mat.uniroma2.it/~sorrenti/Homepage_files/HomogenizationHJ.pdf}, year = {2016}, date = {2016-02-08}, abstract = {Since the celebrated work by Lions, Papanicolaou and Varadhan in 1980’s, there has been a considerable attention to the homogenization problem for Hamilton-Jacobi equation: roughly speaking, how to describe what macroscopic properties and aspects of this equation survive, once all of its local features are neglected (for example, by averaging over faster and faster oscillations). The interest in this question – besides the importance of the Hamilton-Jacobi equation in many different contexts (classical mechanics, symplectic geometry, PDEs, etc...) – has been in recent years boosted by the manifold connections that it shares with new prominent areas of research: Aubry-Mather theory, weak KAM theory, symplectic homogenization, just to mention a few of them. In this article, we discuss a very natural and important question, namely how to extend these classical results beyond the Euclidean setting, which has been recently addressed in a work by Contreras, Iturriaga and Siconolfi. Starting from their result and from the above-mentioned work by Lion, Papanicolaou and Varadhan, we first describe how both of them can be interpreted as a particular case of a more intrinsic and geometric approach, i.e., the case of Tonelli Hamiltonians which are invariant under the action of a discrete group. In particular, we point out the leading role played by the algebraic nature of the group (more specifically, its rate of growth) in driving the homogenization process and determining the features of the limit problem. Then, we prove a homogenization result in the case of Hamiltonians that are invariant under the action of a discrete (virtually) nilpotent group (i.e., with polynomial growth). Besides being more intrinsic and geometric, this novel approach provides a much clearer understanding of the structures of both the limit space and the homogenized equation, unveiling features and phenomena that in the previously-studied cases were shadowed by either the homogeneity of the ambient space or the abelianity of the acting group.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } Since the celebrated work by Lions, Papanicolaou and Varadhan in 1980’s, there has been a considerable attention to the homogenization problem for Hamilton-Jacobi equation: roughly speaking, how to describe what macroscopic properties and aspects of this equation survive, once all of its local features are neglected (for example, by averaging over faster and faster oscillations). The interest in this question – besides the importance of the Hamilton-Jacobi equation in many different contexts (classical mechanics, symplectic geometry, PDEs, etc...) – has been in recent years boosted by the manifold connections that it shares with new prominent areas of research: Aubry-Mather theory, weak KAM theory, symplectic homogenization, just to mention a few of them. In this article, we discuss a very natural and important question, namely how to extend these classical results beyond the Euclidean setting, which has been recently addressed in a work by Contreras, Iturriaga and Siconolfi. Starting from their result and from the above-mentioned work by Lion, Papanicolaou and Varadhan, we first describe how both of them can be interpreted as a particular case of a more intrinsic and geometric approach, i.e., the case of Tonelli Hamiltonians which are invariant under the action of a discrete group. In particular, we point out the leading role played by the algebraic nature of the group (more specifically, its rate of growth) in driving the homogenization process and determining the features of the limit problem. Then, we prove a homogenization result in the case of Hamiltonians that are invariant under the action of a discrete (virtually) nilpotent group (i.e., with polynomial growth). Besides being more intrinsic and geometric, this novel approach provides a much clearer understanding of the structures of both the limit space and the homogenized equation, unveiling features and phenomena that in the previously-studied cases were shadowed by either the homogeneity of the ambient space or the abelianity of the acting group. |

Sorrentino, Alfonso Lecture Notes on Mather's Theory for Lagrangian Systems Journal Article Publicationes Matemática del Uruguay, to appear , 2016. @article{SorrentinoLectureCIMPA2016, title = {Lecture Notes on Mather's Theory for Lagrangian Systems}, author = {Alfonso Sorrentino}, editor = {Ezequiel Maderna and Ludovic Rifford}, url = {http://www.mat.uniroma2.it/~sorrenti/Homepage_files/LectureNotes-Sorrentino_CIMPA.pdf}, year = {2016}, date = {2016-02-08}, journal = {Publicationes Matemática del Uruguay}, volume = {to appear}, abstract = {These notes are based on a series of lectures that the author gave at the CIMPA Research School Hamiltonian and Lagrangian Dynamics, which was held in Salto (Uruguay) in March 2015.}, keywords = {}, pubstate = {published}, tppubtype = {article} } These notes are based on a series of lectures that the author gave at the CIMPA Research School Hamiltonian and Lagrangian Dynamics, which was held in Salto (Uruguay) in March 2015. |

Bianchi, Alessandra; Gaudillière, Alexandre Metastable states, quasi-stationary and soft measures, mixing time asymptotic via variational principles Journal Article Stochastic Processes and their Applications, 126 (6), pp. 1622 - 1680, 2016. @article{Bianchi2015, title = {Metastable states, quasi-stationary and soft measures, mixing time asymptotic via variational principles }, author = {Alessandra Bianchi and Alexandre Gaudillière}, url = {http://arxiv.org/abs/1103.1143 http://www.sciencedirect.com/science/article/pii/S030441491500304X}, doi = {10.1016/j.spa.2015.11.015}, year = {2016}, date = {2016-06-01}, journal = {Stochastic Processes and their Applications}, volume = {126}, number = {6}, pages = {1622 - 1680}, abstract = {We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypotheses for Markov chains on a finite configuration space in some asymptotic regime. By comparing restricted ensembles and quasi-stationary measures, and introducing soft measures as an interpolation between the two, we prove an asymptotic exponential exit law and, on a generally different time scale, an asymptotic exponential transition law. By using potential-theoretic tools, and introducing “(κ,λ)-capacities”, we give sharp estimates on relaxation time, as well as mean exit time and transition time. We also establish local thermalization on shorter time scales.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypotheses for Markov chains on a finite configuration space in some asymptotic regime. By comparing restricted ensembles and quasi-stationary measures, and introducing soft measures as an interpolation between the two, we prove an asymptotic exponential exit law and, on a generally different time scale, an asymptotic exponential transition law. By using potential-theoretic tools, and introducing “(κ,λ)-capacities”, we give sharp estimates on relaxation time, as well as mean exit time and transition time. We also establish local thermalization on shorter time scales. |

Huang, Guan; Kaloshin, Vadim; Sorrentino, Alfonso On marked length spectrums of generic strictly convex billiard tables Unpublished 2016. @unpublished{HuangKaloshinSorrentino2016, title = {On marked length spectrums of generic strictly convex billiard tables}, author = {Guan Huang and Vadim Kaloshin and Alfonso Sorrentino}, url = {http://arxiv.org/abs/1603.08838}, year = {2016}, date = {2016-04-04}, abstract = {In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry-Mather periodic orbits of the induced billiard map, from the (maximal) marked length spectrum of the domain.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry-Mather periodic orbits of the induced billiard map, from the (maximal) marked length spectrum of the domain. |

Cellarosi, Francesco; Munday, Sara On two conjectures for M&m sequences Journal Article Journal of Difference Equations and Applications, 22 (3), pp. 428 - 440, 2016. @article{Cellarosi2016, title = {On two conjectures for M&m sequences}, author = {Francesco Cellarosi and Sara Munday}, url = {http://www.tandfonline.com/doi/abs/10.1080/10236198.2015.1102232}, doi = {10.1080/10236198.2015.1102232}, year = {2016}, date = {2016-01-04}, journal = {Journal of Difference Equations and Applications}, volume = {22}, number = {3}, pages = {428 - 440}, abstract = {In this paper, the recently introduced M&m sequences and associated mean-median map are studied. These sequences are built by adding new points to a set of real numbers by balancing the mean of the new set with the median of the original. This process, although seemingly simple, gives rise to complicated dynamics. The main result is that two conjectures put forward by Chamberland and Martelli are shown to be true for a subset of possible starting conditions. }, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, the recently introduced M&m sequences and associated mean-median map are studied. These sequences are built by adding new points to a set of real numbers by balancing the mean of the new set with the median of the original. This process, although seemingly simple, gives rise to complicated dynamics. The main result is that two conjectures put forward by Chamberland and Martelli are shown to be true for a subset of possible starting conditions. |

Jordan, Thomas; Munday, Sara; Sahlsten, Tuomas Pointwise perturbations of countable Markov maps Unpublished 2016. @unpublished{Jordan2016, title = {Pointwise perturbations of countable Markov maps}, author = {Thomas Jordan and Sara Munday and Tuomas Sahlsten}, url = {http://arxiv.org/abs/1601.06591}, year = {2016}, date = {2016-01-25}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } |

Bianchi, Alessandra; Cristadoro, Giampaolo; Lenci, Marco; Ligabò, Marilena Random walks in a one-dimensional Lévy random environment Journal Article Journal of Statistical Physics, 163 (1), pp. 22 - 40, 2016. @article{Bianchi2016, title = {Random walks in a one-dimensional Lévy random environment}, author = {Alessandra Bianchi and Giampaolo Cristadoro and Marco Lenci and Marilena Ligabò}, url = {http://arxiv.org/abs/1411.0586}, doi = {10.1007/s10955-016-1469-0}, year = {2016}, date = {2016-04-01}, journal = {Journal of Statistical Physics}, volume = {163}, number = {1}, pages = {22 - 40}, abstract = {We consider a generalization of a one-dimensional stochastic process known in the physical literature as L'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process. }, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider a generalization of a one-dimensional stochastic process known in the physical literature as L'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process. |

Mazzucchelli, Marco; Sorrentino, Alfonso Remarks on the symplectic invariance of Aubry-Mather sets Journal Article Comptes Rendus Mathematiques (CRAS), 354 (4), pp. 419 - 423, 2016. @article{MazzSorr2016, title = {Remarks on the symplectic invariance of Aubry-Mather sets}, author = {Marco Mazzucchelli and Alfonso Sorrentino}, url = {http://www.mat.uniroma2.it/~sorrenti/Homepage_files/RemarksSymplecticInvariance.pdf}, year = {2016}, date = {2016-02-08}, journal = {Comptes Rendus Mathematiques (CRAS)}, volume = {354}, number = {4}, pages = {419 - 423}, abstract = {In this note we discuss and clarify some issues related to the generalization of Bernard’s theorem on the symplectic invariance of Aubry, Mather and Mañe sets, to the cases of non-zero cohomology classes or non- exact symplectomorphisms, not necessarily homotopic to the identity. On discute et clarifie quelques questions lièes à la généralisation du théorème de Bernard sur l’invariance symplectique des ensembles d’Aubry, de Mather, et de Mañe, aux cas de classes de cohomologie non nulles et de symplectomorphismes non exacts et pas nécessairement homotopes à l’identité. }, keywords = {}, pubstate = {published}, tppubtype = {article} } In this note we discuss and clarify some issues related to the generalization of Bernard’s theorem on the symplectic invariance of Aubry, Mather and Mañe sets, to the cases of non-zero cohomology classes or non- exact symplectomorphisms, not necessarily homotopic to the identity. On discute et clarifie quelques questions lièes à la généralisation du théorème de Bernard sur l’invariance symplectique des ensembles d’Aubry, de Mather, et de Mañe, aux cas de classes de cohomologie non nulles et de symplectomorphismes non exacts et pas nécessairement homotopes à l’identité. |

Bonanno, Claudio; Isola, Stefano Series expansions for Maass forms on the full modular group from the Farey transfer operators Unpublished 2016. @unpublished{Bonanno2016b, title = {Series expansions for Maass forms on the full modular group from the Farey transfer operators}, author = {Claudio Bonanno and Stefano Isola}, url = {http://arxiv.org/abs/1607.03414}, year = {2016}, date = {2016-07-08}, abstract = {We analyze the relations previously established by Mayer, Lewis-Zagier and the authors, among the eigenfunctions of the transfer operators of the Gauss and the Farey maps, the solutions of the Lewis-Zagier three-term functional equation and the Maass forms on the modular surface SL(2,Z)\H. As main result, we establish new series expansions for the Maass cusp forms and the non-holomorphic Eisenstein series restricted to the imaginary axis.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } We analyze the relations previously established by Mayer, Lewis-Zagier and the authors, among the eigenfunctions of the transfer operators of the Gauss and the Farey maps, the solutions of the Lewis-Zagier three-term functional equation and the Maass forms on the modular surface SL(2,Z)H. As main result, we establish new series expansions for the Maass cusp forms and the non-holomorphic Eisenstein series restricted to the imaginary axis. |

Boscain, Ugo; Prandi, Dario; Seri, Marcello Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds Journal Article Communications in Partial Differential Equations, 41 (1), pp. 32 - 50, 2016. @article{Boscain2015, title = {Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds}, author = {Ugo Boscain and Dario Prandi and Marcello Seri}, url = {http://arxiv.org/abs/1406.6578}, doi = {10.1080/03605302.2015.1095766}, year = {2016}, date = {2016-01-01}, journal = {Communications in Partial Differential Equations}, volume = {41}, number = {1}, pages = {32 - 50}, abstract = {We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator. |

Isola, Stefano Su alcuni rapporti tra matematica e scale musicali Journal Article La matematica nella società e nella cultura. Rivista dell'Unione Matematica Italiana, to appear , 2016. @article{Isola2016, title = {Su alcuni rapporti tra matematica e scale musicali}, author = {Stefano Isola}, url = {http://www.dinamici.org/wp-content/uploads/2016/02/umi-finale.pdf}, year = {2016}, date = {2016-04-01}, journal = {La matematica nella società e nella cultura. Rivista dell'Unione Matematica Italiana}, volume = {to appear}, keywords = {}, pubstate = {published}, tppubtype = {article} } |

## 2015 |

Bonanno, Claudio A complexity approach to the soliton resolution conjecture Journal Article Journal of Statistical Physics, 160 (5), pp. 1432 - 1448, 2015. @article{Bonanno2015, title = {A complexity approach to the soliton resolution conjecture}, author = {Claudio Bonanno}, url = {http://arxiv.org/abs/1407.7570}, doi = {10.1007/s10955-015-1297-7}, year = {2015}, date = {2015-06-18}, journal = {Journal of Statistical Physics}, volume = {160}, number = {5}, pages = {1432 - 1448}, abstract = {The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of solitons plus a radiative term. In this paper we use the complexity of a finite object, a notion introduced in Algorithmic Information Theory, to show that the soliton resolution conjecture is equivalent to the analogous of the second law of thermodynamics for the complexity of a solution of a dispersive equation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of solitons plus a radiative term. In this paper we use the complexity of a finite object, a notion introduced in Algorithmic Information Theory, to show that the soliton resolution conjecture is equivalent to the analogous of the second law of thermodynamics for the complexity of a solution of a dispersive equation. |

Prandi, Dario; Rizzi, Luca; Seri, Marcello 2015. @unpublished{Prandi2015, title = {A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators}, author = {Dario Prandi and Luca Rizzi and Marcello Seri}, url = {http://arxiv.org/abs/1509.05415}, year = {2015}, date = {2015-09-01}, journal = {in review}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } |

# Publications

Search: