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arXiv · 1710.07511

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

Artur O. Lopes·Elismar R. Oliveira
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Abstract

We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, 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 H\"older cocycles. IFS with weights appears in our reasoning in the H\"older case.

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Artur O. Lopes, Elismar R. Oliveira. 2017-10-20. Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator. https://arxiv.org/abs/1710.07511

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