Invariant sets and measures of nonexpansive group automorphisms

Elon Lindenstrauss*, Klaus Schmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageAmerican English
Pages (from-to)29-60
Number of pages32
JournalIsrael Journal of Mathematics
StatePublished - 2004
Externally publishedYes


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