Chaotic Dynamics of the Kepler Problem with Oscillating Singularity

Chaotic Dynamics of the Kepler Problem with Oscillating Singularity Abstract We prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic gravitational coefficient oscillating between two fixed values. The set of chaotic solutions we detect is coded by the number of revolutions in each period. The chaotic dynamics is obtained for large period T as well as for small angular momentum μ. In particular, we provide an explicit lower bound on T and explicit upper bound on μ which guarantee the existence of complex dynamics. We get our results by applying a simple and well-known topological method, the stretching along the path technique. Our results are robust with respect to small perturbations of the gravitational coefficient and to the addition of a small friction term. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Nonlinear Studies de Gruyter

Chaotic Dynamics of the Kepler Problem with Oscillating Singularity

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1536-1365
eISSN
2169-0375
DOI
10.1515/ans-2015-5026
Publisher site
See Article on Publisher Site

Abstract

Abstract We prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic gravitational coefficient oscillating between two fixed values. The set of chaotic solutions we detect is coded by the number of revolutions in each period. The chaotic dynamics is obtained for large period T as well as for small angular momentum μ. In particular, we provide an explicit lower bound on T and explicit upper bound on μ which guarantee the existence of complex dynamics. We get our results by applying a simple and well-known topological method, the stretching along the path technique. Our results are robust with respect to small perturbations of the gravitational coefficient and to the addition of a small friction term.

Journal

Advanced Nonlinear Studiesde Gruyter

Published: Aug 1, 2016

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