Chaos in the Gyldén problem
- 1 December 1998
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 39 (12), 6537-6546
- https://doi.org/10.1063/1.532663
Abstract
We consider the Gyldén problem—a perturbation of the Kepler problem via an explicit function of time. For certain general classes of planar periodic perturbations, after proving a Poincaré–Melnikov-type criterion, we find a manifold of orbits in which the dynamics is given by the shift automorphism on the set of bi-infinite sequences with infinitely many symbols. We achieve the main result by computing the Melnikov integral explicitly.Keywords
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