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

Richard  Sharp

doi:10.3934/dcds.2016.36.2711

Article Contents

2016, Volume 36, Issue 5: 2711-2727. Doi: 10.3934/dcds.2016.36.2711

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

Richard Sharp^1,

1.
Mathematics Institute, University of Warwick, Coventry CV4 7AL

Received: October 31, 2014

Revised: August 31, 2015

Published: May 2017

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Abstract

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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Mathematics Subject Classification: Primary: 28A80, 37C30, 37D35, 58B34; Secondary: 37A55, 37D20, 37F30, 37F35.

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