Stable ergodicity of conservative diffeomorphisms
主 题: Stable ergodicity of conservative diffeomorphisms
报告人: Professor Sylvain Crovisier (University of Paris 11)
时 间: 2016-05-25 15:00 - 16:00
地 点: 理科一号楼 1114(数学所活动）
We will discuss a question about ergodicity of diffeomorphisms preserving the volume on a compact manifold: Does the orbit of almost every point equidistribute withrespect to the volume? On the one hand, Kolmogorov-Arnold-Moser theorems shows that this fails for an open class of diffeomorphisms. On the other hand Anosov has proved that the ergodicity holds for another open class - the set of uniformly hyperbolic systems. More recent works, initiated by Pugh and Shub, have proposed mechanisms implying the ergodicity which are stable under perturbations of the dynamics. In this talk I will present a result joint with A. Avila and A. Wilkinson: the stable ergodicity is satisfied for a C1-dense set of diffeomorphisms in a large class of systems satisfying a weaker notion of hyperbolicity (called partial hyperbolicity).