A Poisson limit theorem for Gibbs-Markov maps

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.

References in corpus (2)

• Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems
• Note on limit distribution of normalized return times and escape rate