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    BARAVIERA, ALEXANDRE LOPES, ARTUR O. and THIEULLEN, PHILIPPE 2006. A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE. Stochastics and Dynamics, Vol. 06, Issue. 01, p. 77.


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  • Ergodic Theory and Dynamical Systems, Volume 24, Issue 4
  • August 2004, pp. 1051-1082

C*-algebras, approximately proper equivalence relations and thermodynamic formalism

  • R. EXEL (a1) and A. LOPES (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385704000148
  • Published online: 01 August 2004
Abstract

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relations and propose the construction of a ‘quotient space’. We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from thermodynamics we prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry–Mather measures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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