Rigidity of center Lyapunov exponents and susu-integrability

  • Shaobo Gan

    Peking University, Beijing, China
  • Yi Shi

    Peking University, Beijing, China
Rigidity of center Lyapunov exponents and $su$-integrability cover
Download PDF

A subscription is required to access this article.

Abstract

Let ff be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism AA on T3\mathbb{T}^3. We show that the stable and unstable bundles of ff are jointly integrable if and only if every periodic point of ff admits the same center Lyapunov exponent with AA. This implies every conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on T3\mathbb{T}^3, is ergodic. This proves the Ergodic Conjecture proposed by Hertz–Hertz–Ures on T3\mathbb{T}^3.

Cite this article

Shaobo Gan, Yi Shi, Rigidity of center Lyapunov exponents and susu-integrability. Comment. Math. Helv. 95 (2020), no. 3, pp. 569–592

DOI 10.4171/CMH/497