A Conservative Partially Hyperbolic Dichotomy: Hyperbolicity versus Nonhyperbolic Measures

报告人：杨佳刚（巴西弗鲁米嫩塞联邦大学）

时  间：2026年5月24日9:00

地  点：腾讯会议: 714-1526-6102 & 行政楼C503

内容摘要:

In a conservative and partially hyperbolic three-dimensional setting, we study three representative classes of diffeomorphisms: those homotopic to Anosov (or Derived from Anosov diffeomorphisms), diffeomorphisms in neighborhoods of the time-one map of the geodesic flow on a surface of negative curvature, and accessible and dynamically coherent skew products with circle fibers. In any of these classes, we establish the following dichotomy: either the diffeomorphism is Anosov, or it possesses nonhyperbolic ergodic measures. Our approach is perturbation-free and combines recent advances in the study of stably ergodic diffeomorphisms with a variation of the periodic approximation method to obtain ergodic measures.

This is a joint work with Lorenzo J. Diaz and Jinhua Zhang.

个人简介：

杨佳刚，巴西弗鲁米嫩塞联邦大学副教授，主要研究领域为动力系统与遍历论，已在Duke Mathematical Journal、Journal of the European Mathematical Society (JEMS)、Advances in Mathematics、 Transactions of the American mathematical Society 、Journal of the Institute of Mathematics of Jussieu、 Ergodic Theory and Dynamical Systems等杂志上发表学术论文30余篇。

联系人：吴伟胜