Nonstandard analysis of asymptotic points of expansive systems

TL;DR

This paper uses nonstandard analysis to characterize the existence of doubly-asymptotic points in expansive dynamical systems, linking it to the decay of expansivity constants.

Contribution

It introduces a novel nonstandard analysis approach to analyze asymptotic points in expansive systems, providing a precise condition for their existence.

Findings

Characterizes doubly-asymptotic points via decay of expansivity constants.

Provides necessary and sufficient condition for doubly-asymptotic points.

Connects nonstandard analysis techniques with dynamical systems theory.

Abstract

In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit doubly-asymptotic points in terms of the decay of expansivity constants of the powers of the system.