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

Nasab Yassine

doi:10.3934/dcds.2018017

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2018, Volume 38, Issue 1: 343-361. Doi: 10.3934/dcds.2018017

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

Nasab Yassine^,

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

* Corresponding author: Nasab Yassine
* Corresponding author: Nasab Yassine

Received: September 2016

Revised: July 2017

Published: October 2017

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Abstract

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.

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Mathematics Subject Classification: Primary:37B20;Secondary:37A50, 60F05.

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