Non Uniformly Hyperbolic Dynamical Systems. Coupling and Renewal Theory (Thematic Month 2017)

We would like to explore the statistical properties of uniformly and non-uniformly hyperbolic dynamical systems in terms of maps and flows,  and also in the framework of Teichmüller dynamics,  with the objective to establish limit theorems using new and promising techiques, including:

• Kontsevich -Zorich cocycles and  Lyapunov exponents.
• Banach anisotropic spaces, which recently allowed to prove the exponential decay of correlations for the Sinai billiard flow.
• Coupling, particularly in the context of the theory of standard families developed by Chernov and Dolgopiat
• Renewal theory with applications to sigma-finite measures.
• Spectral theory of transfer operator, using ideas and methods from  micro-local analysis.

There are also dynamic systems of different nature which exhibit very rich statistical behaviors and which are the subject of intense research nowadays, in particular:

• the  « fast-slow »  systems, with applications to transport theory and « rough paths ».
• Non-autonomous systems, such as sequential or random dynamical systems.
• Open systems, especially in higher dimensions and for perturbed systems, and their connection with the Lyapunov spectra.

Scientific Committee & Organizing Committee

Serge Troubetzkoy (Aix-Marseille Université)
Sandro Vaienti (Aix-Marseille Université et Université de Toulon)

« We the organizers of this conference affirm that scientific events must be open to everyone, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We believe that such events must be supportive, inclusive, and safe environments for all participants. We believe that all participants are to be treated with dignity and respect. Discrimination and harassment cannot be tolerated. We are committed to ensuring that the conference Non Uniformly Hyperbolic Dynamical Systems. Coupling and Renewal Theory follows these principles. For more information on the Statement of Inclusiveness, see this dedicated web page http://www.math.toronto.edu/~rafi/statement/index.html. »

Speakers 

• Romain Aimino (University of Porto)

Random Lorentz gas and deterministic walks in random environments

• Peter Balint​ (TU Budapest)

The system of two falling balls

• Jozef Bobok (Czech Technical University in Prague)

Constant slope maps, the Vere Jones classification, Lipschitz constants and entropy

• ​Henk Bruin (University of Vienna)

The Dolgopyat inequality for BV observables   (slides)

• Keith Burns (Northwestern University)

​Mixing properties of the Weil-Petersson geodesic flow

• Vaughn Climenhaga (University of Houston)

Young towers for surface diffeomorphisms

• ​Yves Coudène (Université de Brest Occidentale)

Generic properties of the geodesic flow in nonpositive curvature

• Sylvain Crovisier (Université Paris-Sud)

Singular hyperbolicity and homoclinic tangencies of 3-dimensional flows

• Jérôme Dedecker (Université Paris Descartes)

Large and Moderate deviations for slowly mixing Markov chains

• ​​Mark Demers (Fairfield University)

Hitting Times and Escape Rates   (slides)

• ​Davor Dragicevic (UNSW Australia)

Almost sure invariance principle for random piecewise expanding maps

• Aihua Fan (Université de Picardie Jules Verne)

​Oscillating sequences realized by dynamical systems

• Frédéric Faure (Université de Grenoble)

Global normal form and asymptotic spectral gap for open partially expanding maps

• Stefano Galatolo (Università di Pisa)

Computer aided results in ergodic theory and Existence of Noise Induced Order   (slides)   Belousov Zhabotinsky reaction (mp4)

• ​Cecilia González Tokman (University of Queensland)

Non-autonomous dynamical systems and multiplicative ergodic theory

• Carangelo Liverani (Universita di Roma « Tor Vergata« )

Fast-Slow partially hyperbolic systems: an example

• Giorgio Mantica (Università dell’Insubria)

Regularity properties of Minkowski’s question mark measure   (slides)

• Ian Melbourne (University of Warwick)

Mixing and rates of mixing for infinite measure flows

• Frédéric Naud (Université Avignon)

Non trivial Ruelle spectrum in uniformly and partially hyperbolic systems   (slides)

• Matthew Nicol (University of Houston)

Dynamical Borel-Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems   (slides)

• Françoise Pène (Université de Brest)

Time-space study of visits to small sets   (slides)

• Mark Pollicott (Warwick University)

Central Limit Theorems for Circle Packings​

• Imre Peter Toth (University of Budapest)

The method of standard pairs in the rare interaction limit of a dynamical heat conduction model

• Jimmy Tseng (University of Bristol)

Ergodic theory and Diophantine approximation for translation surfaces and affine forms​

• Anatoly Vershik (Steklov Institute of Mathematics)

Past of the Markov chains : theory of filtrations

• Hongkun Zhang (University of Massachusetts)

Decay of correlations for various types of billiards with flat points