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Invariant sets and measures of nonexpansive group automorphisms

Elon Lindenstrauss·Klaus Schmidt
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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.

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Elon Lindenstrauss, Klaus Schmidt. 2003-03-11. Invariant sets and measures of nonexpansive group automorphisms. https://arxiv.org/abs/math/0303121

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