Abstract
We study a dynamical system defined by a map of the interval [0, 1] which has 0 as an indifferent fixed point but is otherwise expanding. We prove that the sequence of successive entrance times in a small neighborhood [0,a] converges in law when suitably normalized to a homogeneous Poisson point process.
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Collet, P., Galves, A. Statistics of close visits to the indifferent fixed point of an interval map. J Stat Phys 72, 459–478 (1993). https://doi.org/10.1007/BF01048020
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DOI: https://doi.org/10.1007/BF01048020