Nasab Yassine | Searcharxiv

arXiv2024

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

In this paper, we study the quantitative recurrence properties in the case of $\mathbb{Z}$-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 $\mathbb{Z}$-cover of compact smooth surfaces of negative curvature.

math.DS↗

arXiv2016

Quantitative recurrence of some dynamical systems with an infinite measure in dimension one

We are interested in the asymptotic behaviour of the first return time of the orbits of a dynamical system into a small neighbourhood of their starting points. We study this quantity in the context of dynamical systems preserving an infinite measure. More precisely, we consider the case of $\mathbb{Z}$-extensions of subshifts of finite type. We also consider a toy probabilistic model to enlight the strategy of our proofs.

math.DS↗