Anosov and Circle Diffeomorphisms

  • João P. Almeida
  • Albert M. Fisher
  • Alberto A. Pinto
  • David A. Rand
Part of the Springer Proceedings in Mathematics book series (PROM, volume 1)


We present an infinite dimensional space of C 1 +  smooth conjugacy classes of circle diffeomorphisms that are C 1 +  fixed points of renormalization. We exhibit a one-to-one correspondence between these C 1 +  fixed points of renormalization and C 1 +  conjugacy classes of Anosov diffeomorphisms.


Conjugacy Class Rotation Number Leaf Segment Local Homeomorphism Markov Partition 
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Previous versions of this work were presented in the International Congresses of Mathematicians ICM 2006 and 2010, EURO 2010, ICDEA 2009 and in the celebration of David Rand’s 60th birthday, achievements and influence, University of Warwick. We are grateful to Dennis Sullivan and Flávio Ferreira for a number of very fruitful and useful discussions on this work and for their friendship and encouragement. We thank LIAAD-INESC Porto LA, Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POSI by FCT and Ministério da Ciência e da Tecnologia, and the FCT Pluriannual Funding Program of the LIAAD-INESC Porto LA and of the Research Centre of Mathematics of University of Minho, for their financial support. A. Fisher would like to thank FAPESP, the CNPQ and the CNRS for their financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • João P. Almeida
    • 1
    • 2
    • 3
  • Albert M. Fisher
    • 4
  • Alberto A. Pinto
    • 5
    • 6
  • David A. Rand
    • 7
  1. 1.LIAAD-INESC Porto LAPortoPortugal
  2. 2.Centro de Matemática da Universidade do MinhoBragaPortugal
  3. 3.Departamento de Matemática, Escola Superior de Tecnologia e GestãoInstituto Politécnico de BagançaBragançaPortugal
  4. 4.Departamento de MatemáticaIME-USPSão PauloBrazil
  5. 5.LIAAD-INESC Porto LA e Departamento de Matemática, Faculdade de CiênciasUniversidade do PortoPortoPortugal
  6. 6.Centro de Matemática e Departamento de Matemática e Aplicações, Escola de CiênciasUniversidade do MinhoBragaPortugal
  7. 7.Warwick Systems Biology & Mathematics InstituteUniversity of WarwickCoventryUK

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