Morphisms of Groupoid Actions and Recurrence

TL;DR

This paper explores different types of morphisms between topological groupoid actions and investigates how these morphisms relate to key dynamical properties like recurrence, transitivity, and minimality.

Contribution

It extends the concept of morphisms to continuous groupoid actions and analyzes their impact on various dynamical behaviors.

Findings

Different types of groupoid action morphisms are characterized.

Relations between morphisms and dynamical properties are established.

The study provides a framework for understanding recurrence and minimality in groupoid actions.

Abstract

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms are studied. Among them are recurrence, various forms of transitivity, minimality, limit, recurrent, periodic and almost periodic points.