Work

Almost sure convergence of cover times for $\psi $ -mixing systems

Year: 2025

Type: article

Abstract: Given a topologically transitive system on the unit interval, one can investigate the cover time , that is, the time for an orbit to reach a certain level of resolution in the repeller. We introduce a new notion of dimension, namely the stretched Minkowski dimension , and show that under mixing conditions, the asymptotics of typical cover times are determined by Minkowski dimensions when they are finite, or by stretched Minkowski dimensions otherwise. For application, we show that for countably full-branched affine maps, results using the usual Minkowski dimensions fail to give a finite limit of cover times, whilst the stretched version gives a finite limit. In addition, cover times for irrational rotations are calculated as counterexamples due to the absence of mixing.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10216

Author: BOYUAN ZHAO

Institution: 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

Funder: China Scholarship Council