Co-induction in dynamical systems (Q2908165)

If a countable amenable group \(G\) contains an infinite subgroup \(\Gamma\), one may define from a measurable action of \(\Gamma\), the so called co-induced measurable actions of \(G\). These actions were defined by the first author et al. [Ergodic Theory Dyn. Syst. 28, No. 1, 87--124 (2008;Zbl 1171.37302)]. In this paper, starting from a topological action of \(\Gamma\), the authors define the co-induced topological actions of \(G\). A number of properties are established; notably, the \(G\)-action has the topological entropy of the \(\Gamma\)-action and has uniformly positive entropy (completely positive entropy, respectively) if and only if the \(\Gamma \)-action has uniformly positive entropy (completely positive entropy, respectively). Also, the Pinsker algebra of the co-induced action is studied.