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Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples

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  • For conformal graph directed Markov systems, we construct a spectral triple from which one can recover the associated conformal measure via a Dixmier trace. As a particular case, we can recover the Patterson-Sullivan measure for a class of Kleinian groups.
    Mathematics Subject Classification: Primary: 28A80, 37C30, 37D35, 58B34; Secondary: 37A55, 37D20, 37F30, 37F35.


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