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arXiv · 2512.24151

Transitive partially hyperbolic diffeomorphisms in dimension three

Ziqiang Feng
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Abstract

We prove that any $C^{1+\alpha}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the equivalence between transitivity and ergodicity for $C^{1+\alpha}$ conservative partially hyperbolic diffeomorphisms in \emph{any} closed 3-manifold. Moreover, we provide a characterization of compact accessibility classes under transitivity, thereby giving a precise classification of all accessibility classes for transitive 3-dimensional partially hyperbolic diffeomorphisms.

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Ziqiang Feng. 2025-12-30. Transitive partially hyperbolic diffeomorphisms in dimension three. https://arxiv.org/abs/2512.24151

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