Entry times distribution for dynamical balls on metric spaces (Q2409998)

In this paper the distribution of entry and return times is studied. The authors work with continuous maps on metric spaces. In order to formulate the main result, two properties of the invariant measure are introduced -- mixing property and regularity. Then it is proved that the entry and return times for dynamical balls, such as Bowen balls, are exponential for systems with \( \alpha\)-mixing invariant measure having certain regularities. Examples as Gibbs states for conformal repeller and interval maps are provided. Finally, the obtained results are applied to dynamical systems modeled by a Markov tower such as Young tower.