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arXiv · 2511.00853

Accessibility and central integrability in the absence of periodic points

Ziqiang Feng·Raúl Ures
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Abstract

We consider a partially hyperbolic diffeomorphism $f: M \to M$ without periodic points on a closed manifold $M$. We prove that $f$ is accessible when $M$ is a 3-manifold with non-virtually-solvable fundamental group $\pi_1(M)$. In the case where $\dim E^c = 1$, we demonstrate that the center bundle $E^c$ is uniquely integrable if $f$ lacks accessibility. Furthermore, we provide a complete characterization of accessibility classes for such systems with one-dimensional center bundles.

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Ziqiang Feng, Raúl Ures. 2025-11-02. Accessibility and central integrability in the absence of periodic points. https://arxiv.org/abs/2511.00853

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