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Branches of Periodic Orbits in Reversible Systems

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Recent Trends in Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 35))

Abstract

In the typical reversible systems which appear in many applications (symmetric) periodic solutions appear in one-parameter families. In this short survey we describe how these branches of periodic orbits originate from equilibria, terminate at homoclinic orbits, and branch from each other in period-doubling bifurcations or higher order subharmonic bifurcations. Adding external parameters allows to study degenerate cases and the transition from degenerate to non-degenerate situations.

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References

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Acknowledgements

The more recent work reported in this note has been supported by the University of Sevilla and the MICIIN/FEDER grant number MTM2009-07849.

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Authors and Affiliations

  1. Department of Pure Mathematics, Ghent University, Krijgslaan 281, 9000, Gent, Belgium

    André Vanderbauwhede

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  1. André Vanderbauwhede
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Correspondence to André Vanderbauwhede .

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Editors and Affiliations

  1. Zentrum Mathematik, Technische Universität MĂ¼nchen, Garching bei MĂ¼nchen, Germany

    Andreas Johann

  2. Zentrum Mathematik, Technische Universität MĂ¼nchen, Garching bei MĂ¼nchen, Germany

    Hans-Peter Kruse

  3. Zentrum Mathematik, Technische Universität MĂ¼nchen, Garching bei MĂ¼nchen, Germany

    Florian Rupp

  4. Zentrum Mathematik, Technische Universität MĂ¼nchen, Garching bei MĂ¼nchen, Germany

    Stephan Schmitz

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Vanderbauwhede, A. (2013). Branches of Periodic Orbits in Reversible Systems. In: Johann, A., Kruse, HP., Rupp, F., Schmitz, S. (eds) Recent Trends in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 35. Springer, Basel. https://doi.org/10.1007/978-3-0348-0451-6_3

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