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Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points

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arxiv 2404.07062 v2 pith:N3F3RTEN submitted 2024-04-10 math.DS

Ziqiang Feng , Raúl Ures This is my paper · ORCID
classification math.DS
keywords periodicpointshyperbolicpartiallycloseddiffeomorphismergodicitymanifold
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abstract

We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold $M$ with no periodic points is accessible if the non-wandering set is all of $M$ and the fundamental group $\pi_1(M)$ is not virtually solvable.

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  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

    math.DS 2025-05 conditional novelty 8.0 of 10

    Conservative partially hyperbolic diffeomorphisms homotopic to the identity on closed 3-manifolds with non-virtually-solvable fundamental group are always accessible and hence ergodic.

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