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Renormalization of Circle Diffeomorphism Sequences and Markov Sequences

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Nonlinear Maps and their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 57))

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Abstract

We show a one-to-one correspondence between circle diffeomorphism sequences that are C 1+ n-periodic points of renormalization and smooth Markov sequences.

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References

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Acknowledgements

We acknowledge the financial support of LIAAD-INESC TEC through ‘Strategic Project - LA 14 - 2013–2014’ with reference PEst-C/EEI/LA0014/2013, USP-UP project, IJUP, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, FEDER, POCI 2010 and COMPETE Programmes and Fundação para a Ciência e a Tecnologia (FCT) through Project ‘Dynamics and Applications’, with reference PTDC/MAT/121107/2010. J. P. Almeida acknowledges the support from FCT, given through grant SFRH/PROTEC/49754/2009. Part of this research was done during visits by the authors to IMPA (Brazil), University of Säo Paulo (Brazil), University of Warwick (United Kingdom), Institut Henry Poincaré (France) and SUNY (USA). The authors thank them for their hospitality.

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Authors and Affiliations

  1. LIAAD-INESC TEC and Department of Mathematics, School of Technology and Management, Polytechnic Institute of Bragança, Campus de Santa Apolónia, Ap. 1134, 5301-857, Bragança, Portugal

    João P. Almeida

  2. LIAAD-INESC TEC and Department of Mathematics, University of Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Alberto A. Pinto

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

    David A. Rand

Authors
  1. João P. Almeida
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  2. Alberto A. Pinto
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  3. David A. Rand
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Corresponding author

Correspondence to João P. Almeida .

Editor information

Editors and Affiliations

  1. Colégio Luís António Verney, University of Évora CIMA-UE, Évora, Portugal

    Clara Grácio

  2. LAAS-INSA, Toulouse, France

    Daniele Fournier-Prunaret

  3. Tokushima University, Tokushima, Japan

    Tetsushi Ueta

  4. E. E. Eng., Tokushima University, Tokushima, Japan

    Yoshifumi Nishio

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Almeida, J.P., Pinto, A.A., Rand, D.A. (2014). Renormalization of Circle Diffeomorphism Sequences and Markov Sequences. In: Grácio, C., Fournier-Prunaret, D., Ueta, T., Nishio, Y. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9161-3_1

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