DOI: 10.1017/etds.2026.10356 ISSN: 0143-3857

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 → M $f: M \to M$ f colon upper M right arrow upper 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
π 1 ( M ) $\pi _1(M)$ pi 1 left parenthesis upper M right parenthesis
. In the case where
dim ⁡ E c = 1 $\dim E^c = 1$ dimension upper E Superscript c Baseline equals 1
, we demonstrate that the center bundle
E c $E^c$ upper E Superscript 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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