Elon Lindenstrauss, Klaus Schmidt
Invariant Sets and Measures of Nonexpansive Group Automorphisms
Preprint series: ESI preprints

MSC:

28D05 Measure-preserving transformations

54H15 Transformation groups and semigroups, See also {20M20, 22-XX, 57Sxx}

58F11 Ergodic theory; invariant measures, See also {28Dxx}

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: Nonexpansive group automorphisms, nonhyperbolic toral automorphisms, invariant measures