### Abstract

Original language | English |
---|---|

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 |

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*Ergodic Theory and Dynamical Systems*,

*32*(03), 919-940. https://doi.org/10.1017/S0143385711000083

**Co-induction in dynamical systems.** / Dooley, Anthony H.; Zhang, Guohua.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 32, no. 03, pp. 919-940. https://doi.org/10.1017/S0143385711000083

}

TY - JOUR

T1 - Co-induction in dynamical systems

AU - Dooley, Anthony H.

AU - Zhang, Guohua

PY - 2012/5/3

Y1 - 2012/5/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860713371&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1017/S0143385711000083

U2 - 10.1017/S0143385711000083

DO - 10.1017/S0143385711000083

M3 - Article

VL - 32

SP - 919

EP - 940

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 03

ER -