Invariant sets and measures of nonexpansive group automorphisms
Dynamical Systems
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0303121,
title = {Invariant sets and measures of nonexpansive group automorphisms},
author = {Elon Lindenstrauss and Klaus Schmidt},
journal= {arXiv preprint arXiv:math/0303121},
year = {2007}
}
Comments
28 pages