The Conley index for piecewise continuous maps

TL;DR

This paper extends the Conley index theory to piecewise continuous maps, defining it within compatible isolating neighborhoods, thereby broadening the applicability of topological methods to non-continuous dynamical systems.

Contribution

It introduces a new definition of the Conley index for piecewise continuous maps, accommodating weaker Wazewski properties than in the continuous case.

Findings

Defines the Conley index for piecewise continuous maps.

Establishes conditions for the index to be well-defined.

Provides a framework for analyzing non-continuous dynamical systems.

Abstract

This paper gives the definition of the Conley index for a piecewise continuous map, which is only well defined on compatible isolating neighborhoods with Wazewski property slightly weaker than continuous situation.