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 ‘generic dynamics’
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. [...]
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 [...]
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 [...]
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 [...]
