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KMS states and branched points

Published online by Cambridge University Press:  01 December 2007

MASAKI IZUMI ,
TSUYOSHI KAJIWARA  and
YASUO WATATANI
MASAKI IZUMI
Affiliation:
Department of Mathematics, Graduate School of Sciences, Kyoto University, Kyoto 606-8502, Japan (email: izumi@math.kyoto-u.ac.jp)
TSUYOSHI KAJIWARA
Affiliation:
Department of Environmental and Mathematical Sciences, Okayama University, Tsushima 700-8530, Japan (email: kajiwara@ems.okayama-u.ac.jp)
YASUO WATATANI
Affiliation:
Department of Mathematical Sciences, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan (email: watatani@math.kyushu-u.ac.jp)
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Abstract

We completely classify the Kubo–Martin–Schwinger (KMS) states for the gauge action on a C*-algebra associated with a rational function R introduced in our previous work. The gauge action has a phase transition at β=log deg R. We can recover the degree of R, the number of branched points, the number of exceptional points and the orbits of exceptional points from the structure of the KMS states. We also classify the KMS states for C*-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1887 - 1918
Copyright
Copyright © Cambridge University Press 2007

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