Accessibility and central integrability in the absence of periodic points

2025/11/02 by Feng, Ziqiang, Ures, Raúl
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.00853

Abstract

We consider a partially hyperbolic diffeomorphism f: M → 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 π₁(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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