Dans un travail récemment diffusé sur arxiv, Jana RODRIGUEZ HERTZ montre le théorème suivant: Théorème. Soit un difféomorphisme d’une variété compacte tridimensionnelle, de classe et préservant la mesure volume . Génériquement, vérifie l’une des deux assertions suivantes: -p.p.les trois exposants de Lyapunov sont nuls; -p.p. aucun des trois exposants n’est nul. De plus (a) est [...]
Posts Tagged ‘smooth ergodic theory’
Dichotomie: exposants tous nuls / hyperbolicité et ergodicité
Posted in Dynamics, papers, tagged generic dynamics, partial hyperbolicity, smooth ergodic theory on April 10, 2012 | Leave a Comment »
Continuité de l’entropie
Posted in Dynamics, talks, tagged continuity of the entropy, generic dynamics, measure of maximal entropy, smooth ergodic theory, statistical stability on February 6, 2012 | Leave a Comment »
Dans le cadre du groupe de travail sur les cocycles au-dessus des dynamiques hyperboliques, Jiagang YANG a présenté ce 3 février 2012 ses récents travaux exploitant les propriétés de continuité de l’entropie topologique ou mesurée en fonction de la mesure et/ou de la transformation, notamment pour l’étude de la dynamique générique et de faible régularité. [...]
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 »
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 [...]
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 [...]
A dichotomy for volume-preserving diffeomorphisms in dimension 3
Posted in Dynamics, talks, tagged 3-dimensional diffeomorphisms, dichotomy, ergodicity, Lyapunov exponents, smooth ergodic theory, stable ergodicity on December 6, 2009 | Leave a Comment »
On December 3rd, 2009, M.A. Rodriguez-Hertz presented at the seminar of “Topologie et dynamique” at Orsay a new result extending to three dimensional manifolds the well-known theorem announced by Mañé and proved by Bochi in 2002: Theorem (M.A. Rodriguez-Hertz). Consider the space of all C^1 diffeomorphism preserving the volume on a three-dimensional compact manifold. Then [...]
A measure of maximal entropy (by A. Chéritat)
Posted in Dynamics, tagged Dynamics, maximal entropy measure, pictures, smooth ergodic theory on December 3, 2009 | Leave a Comment »
A measure of maximal entropy of the rational fraction on the Riemann sphere according to Arnaud Chéritat. It describes the distribution of preimages of almost all points.
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 [...]
Sylvain CROVISIER’s HDR
Posted in Dynamics, news, talks, tagged bifurcations, closing lemma, Dynamics, generic dynamics, partial hyperbolicity, smooth ergodic theory, topological dynamics on November 27, 2009 | Leave a Comment »
On November 25th, 2009, Sylvain CROVISIER defended his habilitation à diriger des recherches titled Perturbation de la dynamique de difféomorphismes en petite régularité. He first explained basic perturbation techniques: the Anosov-Katok procedure: you use more and more distorted conjugacies such that the limiting dynamics has new properties; the closing lemma of Pugh and the subsequent [...]
Stable ergodicity and partial hyperbolicity
Posted in Dynamics, talks, tagged Dynamics, partial hyperbolicity, smooth ergodic theory, stable ergodicity on July 6, 2009 | Leave a Comment »
Ya. Pesin gave a talk (Chevaleret, June 19, 2009) summarizing the work on Push-Shub Stable Ergodicity Conjecture and presenting some new results of his in the non-conservative case. This conjecture states that there is a -dense and open set of ergodic diffeomorphisms among those which are partially hyperbolic and volume preserving. Note the tension between [...]
Invisible Attractors
Posted in Dynamics, papers, tagged attractors, Dynamics, smooth ergodic theory on June 22, 2009 | Leave a Comment »
Yu. Ilyashenko and A. Negut have discovered the following dynamical phenomenon. Recall that the statistical attractor is the smallest closed set such that almost every orbit spends almost all its time arbitrarily close to . They say that an open set is -invisible if almost every orbit spends a fraction of its time less than [...]
