Abstract

Topological entropy is often considered as an indicator of complexity. However, determining the positive entropy of multidimensional shifts of finite type lacks a finitely checkable algorithm, as it is right recursively enumerable. In this presentation, we will present the characterization of positive entropy in Markov tree-shifts by adjacency matrices. Additionally, we will reveal the relationship among positive entropy, topological properties, and chaotic behaviors.

 

Organizers: Kuan-Wei Chen (NCTS) & Ryota Mikami (AS)