The cohomology of expansive zd-actions by automorphisms of compact, abelian groups

Anatole B. Katok; Klaus Schmidt

doi:10.2140/pjm.1995.170.105

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

Anatole B. Katok, Klaus Schmidt

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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 Holder cocycle of an expansive and mixing Z^d-action by automorphisms of a compact, abelian group in Hölder cohomologous to a homomorphism.

Original language	English (US)
Pages (from-to)	105-142
Number of pages	38
Journal	Pacific Journal of Mathematics
Volume	170
Issue number	1
DOIs	https://doi.org/10.2140/pjm.1995.170.105
State	Published - Sep 1995

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2140/pjm.1995.170.105

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

Abstract

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