Orbit Representations and Circle Maps

  • Carlos Correia Ramos
  • Nuno Martins
  • Paulo R. Pinto
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)


We yield C*-algebras representations on the orbit spaces from the family of interval maps f(x) = βx+α (mod 1) lifted to circle maps, in which case β ∈ N.

Each orbit will encode an unitary equivalence class of an irreducible representation of: a Cuntz algebra O β if = 0 and β > 1; an irrational rotation algebra A β if α ∉ ℚ and β = 1; and a Cuntz-Krieger O Aα,β whenever β > 1 and the critical point is periodic, where A α,β is the underlying Markov transition matrix of f.


Interval maps irrational rotation algebra Cuntz-Krieger algebra irreducible representations 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Carlos Correia Ramos
    • 1
  • Nuno Martins
    • 2
  • Paulo R. Pinto
    • 2
  1. 1.Departamento de MatemáticaUniversidade de ÉvoraÉvoraPortugal
  2. 2.Centro de Análise Matemática, Geometria e Sistemas Dinâmicos Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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