English

A Poisson limit theorem for Gibbs-Markov maps

Dynamical Systems 2021-04-08 v1

Abstract

We prove for Gibbs-Markov maps that the number of visits to a sequence of shrinking sets with bounded cylindrical lengths converges in distribution to a Poisson law. Applying to continued fractions, this result extends Doeblin's Poisson limit theorem.

Keywords

Cite

@article{arxiv.2010.14365,
  title  = {A Poisson limit theorem for Gibbs-Markov maps},
  author = {Xuan Zhang},
  journal= {arXiv preprint arXiv:2010.14365},
  year   = {2021}
}
R2 v1 2026-06-23T19:41:23.733Z