On The Expansiveness of Lie Group Actions

Elias Rego, Alexander Arbieto

Published 2021-03-11Version 1

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. We investigate the geometric entropy of expansive foliations and prove that any expansive locally-free action of a connected Lie group on a closed manifold has positive geometric entropy. We also study these problems for actions of finely generated groups.