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arXiv · 1609.05791

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

Nasab Yassine
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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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Nasab Yassine. 2016-09-19. Quantitative recurrence of some dynamical systems with an infinite measure in dimension one. https://arxiv.org/abs/1609.05791

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