English

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.

Keywords

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

R2 v1 2026-07-22T16:52:38.551Z