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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.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Nov 2, 2018
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