Ergodic Theory and Dynamical Systems

Research Article

Co-induction in dynamical systems

ANTHONY H. DOOLEYa1 and GUOHUA ZHANGa1a2§

a1 School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia (email: a.dooley@unsw.edu.au)

a2 School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, PR China (email: chiaths.zhang@gmail.com)

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.

(Received September 06 2010)

(Revised January 27 2011)

(Online publication May 24 2011)

Footnotes

§ Corresponding author.