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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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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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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DOI: https://doi.org/10.1007/978-3-0348-0451-6_3
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