Rigidity of center Lyapunov exponents and -integrability

  • Shaobo Gan

    Peking University, Beijing, China
  • Yi Shi

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

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Abstract

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

Cite this article

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

DOI 10.4171/CMH/497