Quantitative recurrence for Z-extension of three-dimensional Axiom A flows

2024/07/12 by Nasab Yassine, Yassine, Nasab
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2407.09058

openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the quantitative recurrence properties in the case of ℤ-extension of Axiom A flows on a Riemannian manifold. We study the asymptotic behavior of the first return time to a small neighborhood of the starting point. We establish results of almost everywhere convergence, and of convergence in distribution with respect to any probability measure absolutely continuous with respect to the infinite invariant measure. In particular, our results apply to geodesic flows on ℤ-cover of compact smooth surfaces of negative curvature.

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