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

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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