Work

A trichotomy for hitting times and escape rates for a class of unimodal maps

Year: 2025

Type: article

Abstract: We consider local escape rates and hitting time statistics for unimodal interval maps of Misiurewicz–Thurston type. We prove that for any point z in the interval, there is a local escape rate and hitting time statistics that is one of three types. While it is key that we cover all points z , the particular interest here is when z is periodic and in the postcritical orbit that yields the third part of the trichotomy. We also prove generalized asymptotic escape rates of the form first shown by Bruin, Demers and Todd.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10201

Authors: MARK DEMERS, MIKE TODD

Institutions: Fairfield University, University of St Andrews

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Fairfield University, Fundação para a Ciência e a Tecnologia