Attractors and chain recurrence in noncompact space for semigroup of continuous maps

TL;DR

This paper explores the concept of chain recurrence and attractors for semigroup actions of continuous maps in noncompact spaces, extending existing definitions and characterizations.

Contribution

It introduces an alternative definition of chain recurrent sets for semigroup actions in noncompact spaces and characterizes them using attractors.

Findings

Provides a new perspective on chain recurrence in noncompact spaces

Extends Conley's attractor characterization to semigroup actions

Clarifies the relationship between chain recurrence and attractors in this setting

Abstract

We shall address the alternative definition of chain recurrent set for the action of a semigroup of continuous self maps, given by M. Hurley \cite {mh} in noncompact space. Following this, we shall address the characterization of chain recurrence in terms of attractors given by C. Conley in \cite {conley}.