Skip to main content
×
Home
    • Aa
    • Aa

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

  • R. EXEL (a1) and A. LOPES (a2)
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.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 6 *
Loading metrics...

Abstract views

Total abstract views: 21 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.