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Rigidity of center Lyapunov exponents and su-integrability
时间  Datetime
2019-08-26 16:00 — 17:00 
地点  Venue
639
报告人  Speaker
史逸
单位  Affiliation
北京大学
邀请人  Host
王晓东
报告摘要  Abstract

Let $f$ be a conservative partially hyperbolic diffeomorphism which is homotopic to an Anosov automorphism $A$ on $T^3$. We show that the stable and unstable bundles of $f$ are jointly integrable if and only if every periodic point of $f$ admits the same center Lyapunov exponent with $A$. In particular, $f$ is Anosov. This implies that every conservative partially hyperbolic diffeomorphism which is homotopic to an Anosov automorphism on $T^3$ is ergodic, which proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on $T^3$. This is a joint work with Shaobo Gan.