Group extensions of Gibbs-Markov maps

Jon Aaronson; Manfred Denker

doi:10.1007/s004400100173

Group extensions of Gibbs-Markov maps

Jon Aaronson^*, Manfred Denker

^*Corresponding author for this work

School of Mathematical Sciences

University of Göttingen

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group double-struck G sign defined on an exact Gibbs-Markov map T : X → X. We show that the group extension T_φ(x, g) = (T(x), g + φ(x)) (x ∈ X; g ∈ double-struck G sign) is exact. Equivalent conditions for exactness are found.

Original language	English
Pages (from-to)	28-40
Number of pages	13
Journal	Probability Theory and Related Fields
Volume	123
Issue number	1
DOIs	https://doi.org/10.1007/s004400100173
State	Published - May 2002

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abstract = "Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group double-struck G sign defined on an exact Gibbs-Markov map T : X → X. We show that the group extension Tφ(x, g) = (T(x), g + φ(x)) (x ∈ X; g ∈ double-struck G sign) is exact. Equivalent conditions for exactness are found.",

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AB - Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group double-struck G sign defined on an exact Gibbs-Markov map T : X → X. We show that the group extension Tφ(x, g) = (T(x), g + φ(x)) (x ∈ X; g ∈ double-struck G sign) is exact. Equivalent conditions for exactness are found.

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Group extensions of Gibbs-Markov maps

Abstract

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