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Bifurcations of symmetric periodic orbits via Floer homology

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Abstract

We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill’s lunar problem.

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Acknowledgements

The authors cordially thank Urs Frauenfelder for introducing to them the paper of Hénon and for helpful discussions on the invariance of the local equivariant Lagrangian Rabinowitz Floer homology and Felix Schlenk for reading a preliminary version very carefully. Special thanks go to anonymous referee for valuable comments. JK is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1901-01. SK is supported by the grant 200021-181980/1 of the Swiss National Foundation. MK is supported by SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics” funded by the DFG.

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea

    Joontae Kim

  2. Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000, Neuchâtel, Switzerland

    Seongchan Kim

  3. Fakultät Für Mathematik, Ruhr-Universität Bochum, IB 3/85, Universitätsstrasse 150, 44801, Bochum, Germany

    Myeonggi Kwon

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  1. Joontae Kim
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Correspondence to Seongchan Kim.

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Communicated by P. Rabinowitz.

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Kim, J., Kim, S. & Kwon, M. Bifurcations of symmetric periodic orbits via Floer homology. Calc. Var. 59, 101 (2020). https://doi.org/10.1007/s00526-020-01757-x

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