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On Families of Periodic Orbits in the Restricted Three-Body Problem

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Abstract

Since Poincaré, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at obvious periodic orbits. On the other hand, given two periodic orbits one might ask if they are connected by an orbit cylinder, i.e., by a one-parameter family of periodic orbits. In this article we study this question for a certain class of periodic orbits in the planar circular restricted three-body problem. Our strategy is to compare the Cieliebak–Frauenfelder–van Koert invariants which are obstructions to the existence of an orbit cylinder.

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  • 28 October 2019

    In this note, we provide a correct formula

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Acknowledgements

The author would like to thank his supervisor Urs Frauenfelder for interesting him in this subject. He is also grateful to Felix Schlenk and Holger Waalkens for valuable discussions, to the unknown referee for valuable comments and to the Institute for Mathematics of University of Augsburg for providing a supportive research environment. This research was supported by DFG Grants CI 45/8-1 and FR 2637/2-1. The results of this paper will form part of the author’s Ph.D. thesis.

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  1. Universität Augsburg, Universitätsstrasse 14, 86159, Augsburg, Germany

    Seongchan Kim

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Kim, S. On Families of Periodic Orbits in the Restricted Three-Body Problem. Qual. Theory Dyn. Syst. 18, 201–232 (2019). https://doi.org/10.1007/s12346-018-0288-x

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