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 language||English (US)|
|Number of pages||38|
|Journal||Pacific Journal of Mathematics|
|State||Published - Sep 1995|
All Science Journal Classification (ASJC) codes