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

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

Author(s) -

Richard Sharp

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2016.36.2711

Subject(s) - conformal map , measure (data warehouse) , markov chain , trace (psycholinguistics) , limit (mathematics) , mathematics , pure mathematics , graph , class (philosophy) , combinatorics , computer science , mathematical analysis , statistics , artificial intelligence , data mining , linguistics , philosophy

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.

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