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Anosov and Circle Diffeomorphisms

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Book cover Dynamics, Games and Science I

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 1))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. LIAAD-INESC Porto LA, Porto, Portugal

    João P. Almeida

  2. Centro de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    João P. Almeida

  3. Departamento de Matemática, Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bagança, Campus de Santa Apolónia, Ap. 1134, 5301-857, Bragança, Portugal

    João P. Almeida

  4. Departamento de Matemática, IME-USP, 66281, CEP 05315-970, São Paulo, Brazil

    Albert M. Fisher

  5. LIAAD-INESC Porto LA e Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Alberto A. Pinto

  6. Centro de Matemática e Departamento de Matemática e Aplicações, Escola de Ciências, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Alberto A. Pinto

  7. Warwick Systems Biology & Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    David A. Rand

Authors
  1. João P. Almeida
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  2. Albert M. Fisher
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  3. Alberto A. Pinto
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  4. David A. Rand
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Corresponding author

Correspondence to João P. Almeida .

Editor information

Editors and Affiliations

  1. Pura e Aplicada (IMPA), Instituto de Matemática, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Rio de Janeiro, Brazil

    Mauricio Matos Peixoto

  2. Faculdade de Ciências, Departamento de Matemática, Universidade do Porto, Rua do Campo Alegre 687, Porto, 4169-007, Portugal

    Alberto Adrego Pinto

  3. Warwick Systems Biology, University of Warwick, Coventry House, Coventry, CV4 7AL, United Kingdom

    David A. Rand

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Almeida, J.P., Fisher, A.M., Pinto, A.A., Rand, D.A. (2011). Anosov and Circle Diffeomorphisms. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science I. Springer Proceedings in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11456-4_2

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