# American Institute of Mathematical Sciences

January  2018, 38(1): 343-361. doi: 10.3934/dcds.2018017

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

 Université de Bretagne Occidentale, LMBA, CNRS UMR 6205, Institut des sciences et Techniques, 29238 Brest Cedex 3, France

* Corresponding author: Nasab Yassine

Received  September 2016 Revised  July 2017 Published  September 2017

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.

Citation: Nasab Yassine. Quantitative recurrence of some dynamical systems preserving an infinite measure in dimension one. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 343-361. doi: 10.3934/dcds.2018017
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