Title: SRB measures for pointwise hyperbolic systems on open regions

Speaker:  Prof. Yunhua Zhou  ( Chongqing University )

Time: Thur, Nov.19 2020, PM: 14:30-15:30

Location:  Tencent Conference

Meeting Number: 982 854 038

Password: 654321

Inviter: Prof. Dongkui Ma

Abstract：

      A diffeomorphism $f: M\to M$ is pointwise partially hyperbolic on an open invariant subset $N\subset M$ if there is an invariant decomposition $T_NM=E^u\oplus E^c\oplus E^s$ such that $D_xf$ is strictly expanding on $E^u_x$ and contracting on $E^s_x$ at each $x\in N$. We show that under certain conditions $f$ has unstable and stable manifolds, and dmits a finite or an infinite $u$-Gibbs measure $\mu$. If $f$ is pointwise hyperbolic on $N$, then $\mu$ is an SRB measure or an infinite SRB measure.  As applications,  we show that some almost Anosov diffeomorphisms and gentle perturbations of Katok's map have the properties. This is a joint work with Jianyu Chen and Huyi Hu.