Viviane Baladi a donné un exposé au séminaire de topologie et dynamique à Orsay sur le problème suivant: Le flot du billard de Sinaï est-il exponentiellement mélangeant? Plus précisément, on considère un point matériel se déplaçant à vitesse constante dans , où est une union finie d’obstacles strictement convexes, lisses, sur le bord desquels s’effectue [...]
Posts Tagged ‘smooth dynamics’
Viviane Baladi: Mélange des flots de contacts hyperboliques par morceaux
Posted in Dynamics, talks, tagged billiards, mixing, smooth dynamics, smooth ergodic theory, transfer on October 16, 2010 | Leave a Comment »
Rafael Potrie: Locally generic Diffeomorphisms With No Attractor
Posted in Dynamics, talks, tagged attractors, generic dynamics, partial hyperbolicity, smooth dynamics on July 5, 2010 | Leave a Comment »
We consider a diffeomorphism where is a compact manifold. A topological attractor is a compact subset which is (i) invariant: ; (ii) chain recurrent: for any , any , there exists a finite sequence such that ; and (iii) whose basin, , is a neighborhood of . This last property can be stated as: it [...]
E. Militon: Distortion elements in groups of smooth diffeomorphisms
Posted in Dynamics, talks, tagged group actions, smooth dynamics on June 7, 2010 | Leave a Comment »
E. Militon explained to the Groupe de travail de théorie ergodique in Orsay the following result. Let be a group. Given and , the length is the minimum length of a product of elements of equal to (possibly ). Definition. is a distortion element if there exists a finite subset , such that . Let [...]
T. Fisher: Diffeomorphisms with Trivial Centralizers
Posted in Dynamics, talks, tagged centralizers, genericity, group actions, hyperbolicity, smooth dynamics, smoothness on June 3, 2010 | Leave a Comment »
A major part of dynamical system theory studies the iteration of diffeomorphisms under various assumptions, geometric or analytic or otherwise. It is also interesting to study them collectively. In particular, , the set of diffeomorphisms of some manifold and some number , is a group. It is for instance of interest to know when it [...]
Dilation factors of pseudo-Anosov homeomorphisms
Posted in Dynamics, talks, tagged Dynamics, flat surfaces, moduli space, pseudo-Anosov, smooth dynamics, surface dynamics, topology on January 14, 2010 | Leave a Comment »
Erwan Lanneau gave a talk in Orsay about his work on surfaces of translation. Pseudo-Anosov homeomorphisms are homeomorphisms of such surfaces which are affine away from the singular set of the surface and whose differential is hyperbolic. The dilation factor is the dominant eigenvalue of that differential. It is a Perron number. The minimum of [...]
C^2 surface diffeomorphisms always have a symbolic extension
Posted in Dynamics, news, papers, tagged Dynamics, entropy, entropy structure, smooth dynamics, smooth ergodic theory, symbolic extension, topological dynamics on December 10, 2009 | Leave a Comment »
Most of topological dynamics studies systems of the form where is a continuous self-map and is a compact metric space. One approach is to “reduce” such systems to symbolic dynamical system, i.e., where is a closed subset of and such that . J. Auslander asked about the obstructions for a topological system to have a [...]
Ergodicity of smooth systems with product measures
Posted in Dynamics, Meetings, talks, tagged entropy, generic dynamics, smooth dynamics, smooth ergodic theory on November 27, 2009 | Leave a Comment »
Federico RODRIGUEZ-HERTZ presented at the IHP conference for Katok’s 65th birthday several results pertaining to the ergodicity of systems with some product structure. Theorem (RHRHTU 2008). Let be a C^2 diffeomorphism of a compact manifold which preserves volume. Let be a hyperbolic periodic point. Define has a transverse point . Define similarly. If and then [...]
Ergodicity of partially hyperbolic symplectomorphisms
Posted in Dynamics, Meetings, talks, tagged Dynamics, ergodic theory, generic dynamics, partial hyperbolicity, smooth dynamics, stable ergodicity on November 27, 2009 | Leave a Comment »
Amie WILKINSON presented new results towards the Pugh-Shub Stable ergodicity conjecture. In particular, with A. AVILA and J. BOCHI, she proved that ergodicity is generic in C^1 partially hyperbolic symplectomorphisms. She noted that, by a result of SAGHIN and Z. XIA, a stably ergodic symplectomorphism is automatically partially hyperbolic (which fails for conservative diffeomorphisms by [...]
