Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous groupoids on the symbolic space, quasi-invariant
  probabilities for Haar systems and the Haar-Ruelle operator   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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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con