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Co-induction in dynamical systems

  • ANTHONY H. DOOLEY (a1) and GUOHUA ZHANG (a1) (a2)
Abstract
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.

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[1] F. Blanchard . Fully positive topological entropy and topological mixing. Symbolic Dynamics and its Applications (Contemporary Mathematics, 135). American Mathematical Society, Providence, RI, 1992, pp. 95105.

[28] P. Walters . An Introduction to Ergodic Theory (Graduate Texts in Mathematics, 79). Springer, New York–Berlin, 1982.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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