Smale Spaces via Inverse Limits

TL;DR

This paper characterizes a class of chaotic dynamical systems called Smale spaces with zero-dimensional contracting directions as stationary inverse limits, providing a new perspective on their structure.

Contribution

It introduces a characterization of irreducible Smale spaces with zero-dimensional contracting directions as stationary inverse limits under specific conditions.

Findings

Identifies conditions under which Smale spaces are stationary inverse limits.

Provides a new framework for understanding the structure of certain Smale spaces.

Abstract

A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale's Axiom A systems are a key class of examples. We consider the special case of irreducible Smale spaces with zero dimensional contracting directions, and characterize these as stationary inverse limits satisfying certain conditions.