Some Properties of Distal Actions on Locally Compact Groups

Details Some Properties of Distal Actions on Locally Compact Groups Some Properties of Distal Actions on Locally Compact Groups

2012-01-20

arxiv.org/abs/1201.4287v1

Mathematics

Dynamical Systems

30 pages

Scientific paper

We show equivalence of distality and pointwise distality of certain actions. We also show that a compactly generated locally compact group of polynomial growth has a compact normal subgroup K such that G/K is distal and the conjugacy action of G on K is ergodic; moreover, if G itself is (pointwise) distal then G is Lie projective. We prove a decomposition theorem for contraction groups of an automorphism under a certain condition. 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 relation between distality, unimodularity and contraction subgroups.

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