Chaos in the Hill system

Details Chaos in the Hill system Chaos in the Hill system

1999-12-02

arxiv.org/abs/gr-qc/9912015v1

Helv.Phys.Acta 72 (1999) 123-157

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages, 6 figures

Scientific paper

We define the general Hill system and briefly analyze its dynamical behavior. A particular Hill system representing the interaction of a Keplerian binary system with a normally incident circularly polarized gravitational wave is discussed in detail. In this case, we compute the Poincar\'e-Melnikov function explicitly and determine its zeros. Moreover, we provide numerical evidence in favor of chaos in this system. The partially averaged equations for the Hill system are used to predict the regular behavior of the Keplerian orbit at resonance with the external radiation.

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