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 language | English |
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Pages (from-to) | 919-940 |
Number of pages | 22 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 32 |
Issue number | 03 |
Early online date | 23 May 2011 |
DOIs | |
Publication status | Published - 3 May 2012 |