The cohomology of expansive ℤ^d-actions by automorphisms of compact, abelian groups

Anatole Katok and Klaus Schmidt

Vol. 170 (1995), No. 1, 105–142

DOI: 10.2140/pjm.1995.170.105

Abstract

Based on the structure of the ℤ^d-actions by automorphisms of compact, abelian groups and on techniques for proving the triviality of the first cohomology of higher rank abelian group actions we prove that, for d > 1, every real-valued Hölder cocycle of an expansive and mixing ℤ^d-action by automorphisms of a compact, abelian group in Hölder cohomologous to a homomorphism.

Mathematical Subject Classification 2000

Primary: 22D40

Secondary: 28D15

Milestones

Received: 7 December 1992

Published: 1 September 1995