Some properties of distal actions on locally compact groups

Article Type

Research Article

Publication Title

Ergodic Theory and Dynamical Systems

Abstract

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We obtain a decomposition for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.

First Page

1340

Last Page

1360

DOI

10.1017/etds.2017.58

Publication Date

5-1-2019

Comments

Open Access, Green

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