Chaos in the Gyldén problem.

Details Chaos in the Gyldén problem. Chaos in the Gyldén problem.

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jmp....39.6537d&link_type=abstract

Journal of Mathematical Physics, Vol. 39, No. 12, p. 6537 - 6546

Mathematics

Mathematical Physics

4

Two-Body Problem: Perturbations

Scientific paper

The authors 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, the authors 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. The authors achieve the main result by computing the Melnikov integral explicitly.

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