Markov partitions reflecting the geometry of x2,x3

TL;DR

This paper provides a geometric description of the , system and analyzes a family of Markov partitions, revealing stability properties and transitions related to non-expansive lines.

Contribution

It introduces an explicit geometric framework for Markov partitions in the , system, connecting their behavior to the system's expansive properties.

Findings

Markov partitions are stable across expansive cones.

Transitions in partition behavior identify non-expansive lines.

The geometric description enhances understanding of the system's dynamics.

Abstract

We give an explicit geometric description of the $\times2,\times3$ system, and use his to study a uniform family of Markov partitions related to those of Wilson and Abramov. The behaviour of these partitions is stable across expansive cones and transitions in this behaviour detects the non-expansive lines.