Invariant sets and measures of nonexpansive group automorphisms

Details Invariant sets and measures of nonexpansive group automorphisms Invariant sets and measures of nonexpansive group automorphisms

2003-03-11

arxiv.org/abs/math/0303121v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of the central foliation is severely restricted. We also prove a topological analogue of this result: the intersection of every proper closed invariant subset with each central leaf is compact.

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