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Piecewise Expanding Maps and Conjugacy Equations

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Nonlinear Maps and their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 112))

Abstract

Topological invariants of interval maps are preserved by conjugacy. We investigate some features of the conjugacy equations associated to piecewise expanding maps. For special cases, it is possible to construct explicitly a conjugacy function in terms of the a-base expansion of numbers through a solution of the corresponding functional equations.

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Acknowledgements

The first author acknowledges support by Fundação para a Ciência e Tecnologia, grant SFRH/BD/77623/2011. The second author acknowledges partial support by Fundação para a Ciência e Tecnologia, PEst-OE/MAT/UI0209/2013. The authors are also indebted to the anonymous referees for their sharp suggestions.

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Authors and Affiliations

  1. Centro de Matemática e Aplicações Fundamentais, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016, Lisboa, Portugal

    Cristina Serpa & Jorge Buescu

Authors
  1. Cristina Serpa
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  2. Jorge Buescu
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Corresponding author

Correspondence to Cristina Serpa .

Editor information

Editors and Affiliations

  1. Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, Spain

    Ricardo López-Ruiz

  2. Université de Toulouse, LAAS-CNRS, INSA, Toulouse, France

    Danièle Fournier-Prunaret

  3. Department of E.E. Eng., Tokushima University, Tokushima, Japan

    Yoshifumi Nishio

  4. Department of Mathematics, University of Évora, CIMA-UE, Évora, Portugal

    Clara Grácio

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Serpa, C., Buescu, J. (2015). Piecewise Expanding Maps and Conjugacy Equations. In: López-Ruiz, R., Fournier-Prunaret, D., Nishio, Y., Grácio, C. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-12328-8_11

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