Systèmes dynamiques non uniformement et partiellement hyperboliques.
Couplage, renouvellement
20 – 24 février, 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.
Comité scientifique & Comité d’organisation

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 »

Random Lorentz gas and deterministic walks in random environments

The system of two falling balls

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

The Dolgopyat inequality for BV observables   (slides)

Mixing properties of the Weil-Petersson geodesic flow

Young towers for surface diffeomorphisms

Generic properties of the geodesic flow in nonpositive curvature

Singular hyperbolicity and homoclinic tangencies of 3-dimensional flows

Large and Moderate deviations for slowly mixing Markov chains

Hitting Times and Escape Rates   (slides)

Almost sure invariance principle for random piecewise expanding maps

  • Aihua Fan (Université de Picardie Jules Verne)

Oscillating sequences realized by dynamical systems

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

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

Non-autonomous dynamical systems and multiplicative ergodic theory

Fast-Slow partially hyperbolic systems: an example

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

Mixing and rates of mixing for infinite measure flows

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

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

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

Central Limit Theorems for Circle Packings​

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

Ergodic theory and Diophantine approximation for translation surfaces and affine forms

Past of the Markov chains : theory of filtrations

Decay of correlations for various types of billiards with flat points