Co-induction in dynamical systems

Anthony H. Dooley, Guohua Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

If a countable amenable group G contains an infinite subgroup Γ, one may define, from a measurable action of Γ, the so-called co-induced measurable action of G. These actions were defined and studied by Dooley, Golodets, Rudolph and Sinelsh’chikov. In this paper, starting from a topological action of Γ, we define the co-induced topological action of G. We establish a number of properties of this construction, notably, that the G-action has the topological entropy of the Γ-action and has uniformly positive entropy (completely positive entropy, respectively) if and only if the Γ-action has uniformly positive entropy (completely positive entropy, respectively). We also study the Pinsker algebra of the co-induced action.
Original languageEnglish
Pages (from-to)919-940
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number03
Early online date23 May 2011
DOIs
Publication statusPublished - 3 May 2012

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