An alternative definition for the Conley relation

TL;DR

This paper introduces a new equivalent definition for the Conley relation in dynamical systems, simplifying its understanding and interpretation within the context of closed relations on compact Hausdorff spaces.

Contribution

It provides a novel, equivalent formulation of the Conley relation, enhancing theoretical clarity in the study of dynamical systems with closed relations.

Findings

New equivalent definition for the Conley relation

Improved interpretation of the Conley relation

Simplification of theoretical framework

Abstract

In the theory of dynamics of closed relations on compact Hausdorff spaces, the definition for the Conley relation $f^\Omega$ of an iterated closed relation $f$ is nontrivial. This paper establishes a new equivalent definition for $f^\Omega$, and discusses its interpretation.