主 题: 动力系统讨论班——Lyapunov exponents, quasiconformality and rigidity in partially hyperbolic systems
报告人: Disheng Xu (The?University of Chicago)
时 间: 2017-09-27 15:10-17:10
地 点: 二教408
Abstract: In the study of hyperbolic behavior in dynamical systems, people have observed some rigidity phenomena caused by equality of Lyapunov exponents for associated cocycles : roughly speaking, if extremal Lyapunov exponents for a cocycle A are equal, then A should satisfy some uncommon dynamical properties.
In this talk we will firstly show a superrigidity phenomenon for perturbation of time-one map of geodesic flow of constantly negatively curved manifold which caused by equality of Lyapunov exponents and quasiconformality of associated dynamics.
The techniques apply more generally to a class of conservative partially hyperbolic diffeomorphisms. It is well-known that the central foliations of partially hyperbolic systems are rarely smooth. Under assumption of quasiconformality, one could prove the smoothness of centre foliations. This is a joint work with C. Butler.
As an application, we get a new rigidity result for higher rank conservative partially hyperbolic action. This is a joint work with D. Damjanovic.