Research-Rigidity of center Lyapunov exponents and su-integrability

Research

Dynamical Systems Seminar

Rigidity of center Lyapunov exponents and su-integrability

Speaker: SHI Yi (Peking University)
Time: Mar 25, 2019, 11:00-12:00
Location: Conference Room 415, Hui Yuan 3#

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. Thus every conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on T^3, is ergodic. This proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on T^3. This is a joint work with Shaobo Gan.