Relativistic effects in the chaotic Sitnikov problem

Kovacs, T.; Bene, G.; Tel, T.

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Relativistic effects in the chaotic Sitnikov problem

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Kovacs, T.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Kovacs, T., Bene, G., & Tel, T. (2011). Relativistic effects in the chaotic Sitnikov problem. Monthly Notices of the Royal Astronomical Society, 414(3), 2275-2281.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-8C87-7

Abstract

We investigate the phase-space structure of the relativistic Sitnikov problem in the first post-Newtonian approximation. The phase-space portraits show a strong dependence on the gravitational radius which describes the strength of the relativistic pericentre advance. Bifurcations appearing at various gravitational radii are presented. Transient chaotic behaviour related to escapes from the primaries is also studied. Finally, the numerically determined chaotic saddle is investigated in the context of hyperbolic and non-hyperbolic dynamics as a function of the gravitational radius.