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Continuous Groupoids on the Symbolic Space, Quasi-Invariant Probabilities for Haar Systems and the Haar–Ruelle Operator

Continuous Groupoids on the Symbolic Space, Quasi-Invariant Probabilities for Haar Systems and... We consider groupoids on $$\{1,2,\ldots ,d\}^\mathbb {N}$$ { 1 , 2 , … , d } N , cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We assume a mild compatibility of the groupoid with the symbolic structure. We present a generalization of the Ruelle operator—the Haar–Ruelle operator—taking into account the Haar structure. We consider continuous and also Hölder cocycles. IFS with weights appears in our reasoning in the Hölder case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Continuous Groupoids on the Symbolic Space, Quasi-Invariant Probabilities for Haar Systems and the Haar–Ruelle Operator

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-018-00123-y
Publisher site
See Article on Publisher Site

Abstract

We consider groupoids on $$\{1,2,\ldots ,d\}^\mathbb {N}$$ { 1 , 2 , … , d } N , cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We assume a mild compatibility of the groupoid with the symbolic structure. We present a generalization of the Ruelle operator—the Haar–Ruelle operator—taking into account the Haar structure. We consider continuous and also Hölder cocycles. IFS with weights appears in our reasoning in the Hölder case.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Nov 2, 2018

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