A Lane from Ergodicity to 3-manifold Topology, and Back
Time: 2024-11-26
Published By: He Liu
Speaker(s): Ziqiang Feng(BICMR)
Time: 15:00-16:00 November 28, 2024
Venue: Room 77201, Jingchunyuan 78, BICMR
Using the argument introduced by Hopf, the so-called "Hopf argument", and developed by Anosov and Sinai, it is well-known that all $C^2$ volume-preserving uniformly hyperbolic systems are ergodic. The Stable Ergodicity Conjecture proposed by Pugh-Shub provides the abundance of ergodic partially hyperbolic diffeomorphisms in dimension three. However, it is still far from clarifying which partially hyperbolic diffeomorphism is ergodic. I will give a glance of how ergodicity traps in 3-manifold topology and how it might survive.
