Events

The school “Algebraic, Geometric and Probabilistic Aspects of Dynamical Systems and Control Theory” will be held at ICTP Trieste, 4 - 15 July 2016.

Courses: Counting Techniques (S. Filip), Introduction to smooth group actions and rigidity (F. Hertz), Symbolic dynamics for low-dimensional systems with positive entropy (Y. Lima), Dynamics of group actions on homogeneous spaces (A. Mohammadi), Kerov-Vershik method in Pickrell’s classification (Y. Qiu), Brownian motion, evolving geometries and entropy formulas (A. Thalmaier).

Thursday 9th June, h 16:00

Aula Magna, Dipartimento di Matematica, Pisa

Vitaly Bergelson (Ohio State University)

“Ergodic Ramsey Theory: the Meeting point of Dynamics and Combinatorics”

Abstract: The goal of this talk is to demonstrate the dynamical underpinning of some old and new results in combinatorics and number theory. The results to be discussed include Schur’s theorem on Fermat equation over finite fields, theorems of van der Waerden and Szemeredi on arithmetic progressions and some of modern developments involving multiple recurrence along polynomials and applications to the patterns in primes.

The workshop “Analytical Methods in Classical and Quantum Dynamical Systems” will be held in Pisa, from June 27 until July 2, 2016, at the Centro “De Giorgi”.

For all information see https://www.crm.sns.it/event/361/index.html#title

Prof. Heinz Hanssmann (University of Utrecht)

“Families of hyperbolic Hamiltonian tori”

Thursday 11 February 2016,  15.00

Dipartimento di Matematica (aula Dal Passo) Università di Roma “Tor Vergata”

Abstract:

In integrable Hamiltonian systems hyperbolic tori form families, parametrised by the actions conjugate to the toral angles. The union over such a family is a normally hyperbolic invariant manifold. Under Diophantine conditions a hyperbolic torus persists a small perturbation away from integrability. Locally around such a torus the normally hyperbolic invariant manifold is the centre manifold of that torus and persists as well. We are interested in `global’ persistence of the normally hyperbolic invariant manifold. An important aspect is how the dynamics behaves at the (topological) boundary. Where the manifold extends to infinity this boundary is empty – this case makes clear that we need the persistence theorem of normally hyperbolic invariant manifolds in the non-compact setting. If the normal hyperbolicity wanes as the boundary is approached we need to ensure that the perturbed dynamics does not come closer to the boundary. This provides the necessary uniform lower bound of normal hyperbolicity to still ascertain persistence under small perturbations. Making use of energy preservation and of Diophantine tori persisting by KAM theory this can be achieved for families of two-dimensional hyperbolic tori.

The workshop “Dynamical systems in logic, complex analysis and ergodic theory” will be held in Pisa, from February 8 until 9, 2016.

For all information see https://pagine.dm.unipi.it/workshoppra/

Wednesday 27th January 2016, h 15:00

Sala Conferenze, Collegio Puteano, Centro De Giorgi, Pisa

Anna Miriam Benini (University of Roma Tor Vergata)

“Permutable entire functions and multiply connnected wandering domains”

Abstract: Let f and g be permutable transcendental entire functions. It is a long standing question whether the Julia sets of f and g are equal. The conjecture is true in the case that f,g are rational functions, and in the transcendental case the main issues are due to the presence of Baker Domains and Wandering Domains. Using a recent analysis of the dynamical behaviour in multiply connected wandering domains, we can make progress by showing that J(f) = J(g) unless (possibly) either f or g has a special type of wandering domains, namely simply connected wandering domain in the fast escaping set. This is joint work with G. Stallard and P. Rippon.

The conference “Renormalization in Dynamics” will be held in Pisa, from April 4 until 8, 2016.

For all information see https://www.crm.sns.it/event/360/

There will be financial support for PhD students and young PostDocs. The deadline for application is 15th January 2016.

Thursday 12th November 2015, h 9:30 Sala Conferenze, Collegio Puteano, Centro De Giorgi, Pisa

Henk Bruin (University of Vienna)

“Sharp mixing rates via inducing with respect to general return times”

Abstract: For non-uniformly expanding maps inducing w.r.t. a general (i.e., not necessarily first) return time to Gibbs Markov maps, we provide sufficient conditions for obtaining sharp estimates for the correlation function. This applies to both the finite and the infinite measure setting. The results are illustrated by non-Markov intervals maps with an indifferent fixed point. This is joint work with Dalia Terhesiu.

Monday 9th November 2015, h 15:00 - 17:00 Aula Seminari (Dipartimento di Matematica, Pisa)

Alfonso Sorrentino (Università di Roma “Tor Vergata”)

“AUBRY-MATHER THEORY FOR TWIST MAPS AND BILLIARDS”

This is a special meeting of the “Mathematical Physics Working Group” of the Mathematical Department of the University of Pisa, and will be of introductory level.

The conference “Geometric Aspects of Modern Dynamics” will be held in Oporto (Portugal) from January 11 until 15, 2016:

https://cmup.fc.up.pt/complexdynamics/

Organizing Committee: Jasmin Raissy (U. Toulouse, France) Helena Reis (U. Porto, Portugal)

Scientific Committee: Marco Abate (U. Pisa, Italy) Alexey Glutsuyk (ENS-Lyon, France) Misha Lyubich (SUNY-SB, US) Julio Rebelo (U. Toulouse, France) Helena Reis (U. Porto, Portugal)