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

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.

keywords: Return time quantitative recurrence local limit theorem

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