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Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three-Body Problem – A Computer Assisted Proof

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Abstract:

 The restricted circular three-body problem is considered for the following parameter values C=3.03, μ=0.0009537 – the values for the Oterma comet in the Sun-Jupiter system. We present a computer assisted proof of an existence of a homo- and heteroclinic cycle between two Lyapunov orbits and an existence of symbolic dynamics on four symbols built on this cycle.

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Authors and Affiliations

  1. GSB – NLU, Faculty of Computer Science, Department of Computational Mathematics, ul. Zielona 27, 33-300 Nowy Sa¸cz, Poland. E-mail: dwilczak@wsb-nlu.edu.pl, , , , , , PL

    Daniel Wilczak

  2. Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland. E-mail: zgliczyn@im.uj.edu.pl, , , , , , PL

    Piotr Zgliczynski

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  1. Daniel Wilczak
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  2. Piotr Zgliczynski
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Received: 15 April 2002 / Accepted: 16 May 2002 Published online: 20 January 2003

RID="*"

ID="*" Research supported in part by Polish KBN grant 2 P03A 011 18, NSF grant DGE-98-04459 and PRODYN.

Communicated by G. Gallavotti

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Wilczak, D., Zgliczynski, P. Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three-Body Problem – A Computer Assisted Proof. Commun. Math. Phys. 234, 37–75 (2003). https://doi.org/10.1007/s00220-002-0709-0

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  • DOI: https://doi.org/10.1007/s00220-002-0709-0

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