Quantitative recurrence properties for systems with non-uniform structure

TL;DR

This paper provides quantitative estimates of recurrence properties in systems with non-uniform structure, applicable to various symbolic systems like beta-shifts and S-gap shifts, enhancing understanding of their recurrence behavior.

Contribution

It introduces new quantitative recurrence estimates for non-uniform symbolic systems, extending analysis to beta-shifts, S-gap shifts, and their factors.

Findings

Quantitative recurrence estimates for non-uniform symbolic systems

Applicability to beta-shifts and S-gap shifts

Extension to factors of these systems

Abstract

Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their factors.