Estimations of topological entropy for non-autonomous discrete systems

TL;DR

This paper provides methods to estimate the bounds of topological entropy for non-autonomous discrete systems, enhancing understanding of their complexity through topological conjugacy and transition matrices.

Contribution

It introduces new estimation techniques for topological entropy bounds in coupled-expanding systems and relates them to subshifts of finite type.

Findings

Lower bounds for topological entropy are established for coupled-expanding systems.

Upper and lower bounds are derived for systems in compact metric spaces.

Topological equi-semiconjugacy links these systems to subshifts of finite type.

Abstract

In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for systems in compact metric spaces are obtained by their topological equi-semiconjugacy to subshifts of finite type under certain conditions.