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. This implies 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.

(Link: https://arxiv.org/pdf/1905.07896.pdf)

Papers Published：                                                                                              

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

[2] Gan, Shaobo; Shi, Yi. Cr-Closing lemma for partially hyperbolic diffeomorphisms with one-dimensional center bundle. arXiv: 2004.06855

       Prof. Gan Shaobo