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Chaos in the Hill system

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Title: Chaos in the Hill system
Author: Chicone, Carmen Charles; Mashhoon, Bahram; Retzloff, David
Keywords: close binaries
gravitational radiation
chaotic motions
relativistic effects
Date: 1999-12
Publisher: arXiv
Citation: arXiv:gr-qc/9912015v1
Abstract: 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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