Expansive Lie Group Actions

TL;DR

This paper introduces the concept of expansiveness for connected Lie group actions, explores its properties, implications, and related concepts like CW-expansiveness, and demonstrates its impact on geometric entropy in foliations and group actions.

Contribution

It defines and analyzes expansiveness for Lie group actions, investigates properties and implications, and links it to geometric entropy, extending the theory of dynamical systems.

Findings

Expansiveness for Lie group actions is well-defined and studied.

Expansiveness implies positive geometric entropy in certain foliations.

CW-expansiveness is introduced for pseudo-group actions.

Abstract

In this work we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some implications of expansiveness. We study the centralizer of expansive actions and introduce CW-expansiveness for pseudo-group actions. As an application, we prove positiveness of geometric entropy for expansive foliations and expansive group actions.