Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator

2017/10/20 by Lopes, Artur O., Oliveira, Elismar R.
#37D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1710.07511

Abstract

We consider groupoids on \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.

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