# Giornata Analisi Armonica, Probabilita’, e Sistemi Dinamici (16 aprile 2018)

Giornata di Analisi Armonica, Probabilita’, e Sistemi Dinamici

Location: Aula 1E (palazzina E)
Dipartimento SBAI (Universita’ di Roma “La Sapienza”)
via A. Scarpa 14, Roma

Lunedi’ 16 aprile:

ore 14:30
Alexander BUFETOV (CNRS & STEKLOV INSTITUTE MOSCOW)
“QUASI-SIMMETRIE DEI PROCESSI DETERMINANTALI”

ore 15:30
Yanqi QIU (CNRS & CHINESE ACADEMY OF SCIENCE)
“DETERMINANTAL PROCESSES IN HYPERBOLIC SPACES”

ore 16:30
Pavel NIKITIN (STEKLOV INSTITUTE ST-PETERSBURG)
“RIGIDITY FOR PFAFFIAN POINT PROCESSES

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement N°647133)”

# Summer School in Dynamics at ICTP, 16-27 July 2018

A Summer School in Dynamical Systems which will be held at ICTP, Trieste (Italy) on 16-27 July 2018.
The school is targeted to Masters and beginning PhD students and aims at introducing a variety of fundamental ideas and techniques in dynamics. The first week will not assume prior knowledge in the field of dynamical systems. Students can also register for the second week only.
Female students are especially encouraged to apply. A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries.
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Organizers and lectures:
-Jana RODRIGUEZ-HERTZ (Southern University of Science and Technology of China)
-Corinna ULCIGRAI (University of Bristol, UK)
-Amie WILKINSON (University of Chicago, USA)
Local organizer: Stefano Luzzatto (ICTP)
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Week 1
A circle of concepts and methods in dynamics.
Basic concepts in dynamics will be introduced, with many examples, especially in the setting of circle maps. Topics include rotations of the circle, doubling map, Gauss map and continued fractions and an introduction to the basic ideas of symbolic codings and invariant measures. At the end of the week we will discuss some simple examples of structural stability and renormalization.
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Week 2
Ergodicity in smooth dynamics (10h, Jana Rodriguez-Hertz and Amie Wilkinson)
The concept of ergodicity is a central hypothesis in statistical mechanics, one whose origins can be traced to Boltzmann’s study of ideal gases in the 19th century. Loosely speaking, a dynamical system is ergodic if it does not contain any proper subsystem, where the notion of “proper” is defined using measures. A powerful theorem of Birkhoff from the 1930’s states that ergodicity is equivalent to the property that “time averages = space averages:” that is, the average value of a function taken along an orbit is the same as the average value over the entire space. The property of ergodicity is the first stepping stone in a path through the study of statistical properties of dynamical systems, a field known as Ergodic Theory.
We will develop the ergodic theory of smooth dynamical systems, starting with the fundamental, linear examples of rotations and doubling maps on the circle introduced in Week 1. We will develop some tools necessary to establish ergodicity of nonlinear smooth systems, such as those investigated by Boltzmann and Poincaré in the dawn of the subject of Dynamical Systems. Among these tools are distortion estimates, density points, invariant foliations and absolute continuity. Closer to the end of the course, we will focus on the ergodic theory of Anosov diffeomorphisms, an important family of “toy models” of chaotic dynamical systems.

Renormalization in entropy zero systems (5h, Corinna Ulcigrai)
Rotations of the circle are perhaps the most basic examples of low complexity (or “entropy zero”) dynamical systems. A key idea to study systems with low complexity is renormalization. The Gauss map and continued fractions can be seen as a tool to renormalize rotations, i.e.study the behaviour of a rotation on finer and finer scales. We will see two more examples of renormalization in action.
The first is the characterization of Sturmian sequences, which arise as symbolic coding of trajectories of rotations (and hint at more recent developments, such as the characterization of cutting sequences for billiards in the regular octagon). The second concerns interval exchange maps (IETs), which are generalizations of rotations. We will introduce the Rauzy-Veech algorithm as a tool to renormalize IETs. As applications, we will give some ideas of how it can be used (in some simplified settings) to study invariant measures and (unique) ergodicity and deviations of ergodic averages for IETs.
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Tutorial and exercise sessions will be held regularly and constitute an essential part of the school.
Tutors: Oliver BUTTERLEY (ICTP), Irene PASQUINELLI (Durham University, UK), Davide RAVOTTI, (University of Bristol, UK), Lucia SIMONELLI (ICTP), Kadim WAR (Ruhr-Universität, Bochum, Germany).
Women in Mathematics: Activities directed to encourage and support women in mathematics, such as panel discussions and small groups mentoring and networking, will be organized during the event.
2 April 2018 (for applicants requesting financial support)
25 June 2018 (for applicants NOT requesting financial support)

Please note the fast-approaching DEADLINE (2 April 2018) for applicants requesting financial support!

# School “Stable and Chaotic Motions in the Planetary Problem”

The school:

“Stable and Chaotic Motions in the Planetary Problem”

will take place in Asiago (Italy), June 10-15 2018, funded by the homonym ERC project Stable and Chaotic Motions in the Planetary problem.

The aim of this school is to study in depth the dynamics of planetary
systems from  the underlying mathematical theories coming from perturbation theories and going back to A. N. Kolmogorov,  V. I. Arnold and J. Moser, up to the recent astronomical observations of comets, asteroids and exoplanets from ground and space.

We foresee 18 hourly mathematical and 10 astronomical lectures.

a) The Mathematical Lectures:
-Alessandra Celletti, Univ. Tor Vergata, Roma (lectures on KAM Theorem);
-Vadim Kaloshin, University of Maryland & ETH, Zurigo (Arnold diffusion);
-Richard Moeckel, University of Minnesota (the N-Body problem);
-Tere Seara, UPC, Barcellona (Arnold diffusion);

b) The Astronomical Lectures (10 hours):
-Alessandro Morbidelli, Observatoire de la Coste d’Azure, Nice (evolution of planetary systems)
-Ivano Bertini, University of Padova (space missions, comets);
-Foriangela La Forgia, University of Padova (comets);
-Francesco Marzari, University of Padova (extrasolar planets dynamics)

The precise titles and abstracts will be soon announced.
The lectures will be held at the Astrophysical Observatory in Asiago.

If you are interested to participate, please register by sending an e-mail to asiagoschool@math.unipd.it, by includig also a short CV, before 30 April.

The participation to the school is open to Phd students, Post doc researchers and researchers. We strongly encourage the participation of Phd and Post-Doc researchers. We will be able to cover the local expenses for a limited number of young participants: to apply for financial support please mention it in the registration e-mail.

The selection of the participants and of the financial support will
be confirmed by e-mail.

Accomodation: a limited number of rooms (cheap, from 10 to 15 euros per day, but comfortable; with kithchen facility) are available in the guest rooms at the Observatory. Further information on other possible accomodations will be soon available.

Please feel free to forward this information to anyone you know who might be interested.

The organizing committee: Cesare Barbieri, Giancarlo Benettin, Massimiliano Guzzo, Monica Lazzarin, Gabriella Pinzari

# Perspectives in Hamiltonian Dynamics (Venice, June 18-22)

“Perspectives in Hamiltonian dynamics”

will be held in Venice (Italy) June 18-22 2018, funded by the homonym ERC project Stable and Chaotic Motions in the Planetary problem.

The aim of this conference is to gather specialists working in the fields of Hamiltonian systems, with a focus on near integrable systems, celestial mechanics, perturbative techniques, Kolmogorov-Arnold-Moser and Nekhorossev theories, Arnold instability.

The following speakers confirmed their participation:

Massimiliano Berti (Scuola Italiana di Studi Superiori Avanzati, Trieste)
Alessandra Celletti (Universita Tor Vergata, Roma)
Alain Chenciner (Institut de mécanique céleste et de calcul des Ephemerides, Paris)
Amadeu Delshams (Universitat Politècnica de Catalunya, Barcelona)
Holger Dullin (University of Sydney)
Bassam Fayad (Institut de Mathématiques de Jussieu, Paris)
Marian Gidea (Yeshiva University, New York)
Giovanni Gronchi (Universita di Pisa)
Marcel Guardia (Universitat Politècnica de Catalunya, Barcelona)
Sergei Kuksin (Universit? Paris-Diderot)
Jacques Laskar (Institut de mécanique céleste et de calcul des ephemerides, Paris)
Elena Lega (Observatoire de la Cote d’Azur)
Jean-Pierre Marco (Université Pierre et Marie Curie, Paris)
Richard Moeckel (University of Minnesota)
Gabriella Pinzari (Universita di Padova)
Tere M.Seara (Universitat Politècnica de Catalunya, Barcelona)
Alfonso Sorrentino (Universita Tor Vergata, Roma)
Dimitri Treschev (Steklov Mathematical Institute of Russian Academy of Sciences)
Dimitri Turaev (Imperial College, London)

If you wish to participate, please register by sending an e-mail to venice2018@math.unipd.it by May 15, 2018.

We foresee a limited number of slots for contributed talks and will be able to cover local expenses for a limited number of young participants. To apply for contributed talk/financial support please register early in advance (before April 30, 2018) and mention
it in the registration e-mail and include a short CV.
The selection of contributed talks and of the financial support will
be confirmed by e-mail.

Full information concerning the location and accommodation will follow.

A tentative web-page including minimal information is here:
https://ercprojectpinzari.wordpress.com/conference-in-venice-18-22-june-2018/
A full web-page is still under construction and will be publicized in a next announcement.

The organizing committee:

Francesco Fasso`, Massimiliano Guzzo, Vadim Kaloshin and Gabriella Pinzari