Heteroclinic Phenomena in the Sitnikov Problem

Details Heteroclinic Phenomena in the Sitnikov Problem Heteroclinic Phenomena in the Sitnikov Problem

Oct 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000hscm.conf..174g&link_type=abstract

HAMILTONIAN SYSTEMS AND CELESTIAL MECHANICS (HAMSYS-98). Proceedings of the III International Symposium. Held 7-11 December 1998

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

We give the deduction of a Melnikov function for the Sitnikov problem. Using a perturbation method introduced by Melnikov and a thorough analysis of the geometry of certain auxiliary functions that we introduce, we prove analytically the existence of transverse heteroclinic orbits. As a consequence, we can embed a Bernoulli shift near these orbits. This shows that the Sitnikov problem possesses chaotic dynamics.

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