Chaos in the Hill system
General Relativity and Quantum Cosmology
2007-05-23 v1 Astrophysics
Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.gr-qc/9912015,
title = {Chaos in the Hill system},
author = {C. Chicone and B. Mashhoon and D. G. Retzloff},
journal= {arXiv preprint arXiv:gr-qc/9912015},
year = {2007}
}
Comments
35 pages, 6 figures