Limit sets and a problem in dynamical systems

TL;DR

This paper explores how chain recurrent dynamical systems can be approximated by periodic systems, drawing parallels to the Bohr theorem on almost periodic functions, to advance understanding of dynamical behavior approximation.

Contribution

It introduces a method to approximate chain recurrent systems with periodic ones, extending classical approximation results to dynamical systems.

Findings

Successful approximation of chain recurrent systems by periodic systems

Extension of Bohr's theorem to dynamical systems context

Potential applications in analyzing complex dynamical behaviors

Abstract

We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.