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Dissipative conformal measures on locally compact spaces

Published online by Cambridge University Press:  10 November 2014

KLAUS THOMSEN
KLAUS THOMSEN*
Affiliation:
Institut for Matematik, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark email matkt@imf.au.dk
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Abstract

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 2 , April 2016 , pp. 649 - 670
Copyright
© Cambridge University Press, 2014 

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