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arXiv · 1905.07896

Rigidity of center Lyapunov exponents and $su$-integrability

Shaobo Gan·Yi Shi
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Abstract

Let $f$ be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism $A$ on $\mathbb{T}^3$. 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 $\mathbb{T}^3$, is ergodic. This proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on $\mathbb{T}^3$.

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Shaobo Gan, Yi Shi. 2019-05-20. Rigidity of center Lyapunov exponents and $su$-integrability. https://arxiv.org/abs/1905.07896

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