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

Anatole B. Katok, Klaus Schmidt

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Abstract

Based on the structure of the Zd 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 Zd-action by automorphisms of a compact, abelian group in Hölder cohomologous to a homomorphism.

Original languageEnglish (US)
Pages (from-to)105-142
Number of pages38
JournalPacific Journal of Mathematics
Volume170
Issue number1
DOIs
StatePublished - Sep 1995

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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