Relativistic effects in the chaotic Sitnikov problem

Details Relativistic effects in the chaotic Sitnikov problem Relativistic effects in the chaotic Sitnikov problem

2011-03-31

arxiv.org/abs/1103.6189v1

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

8 pages, 11 figures

Scientific paper

10.1111/j.1365-2966.2011.18546.x

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 increasing the gravitational radius are presented. Transient chaotic behavior related to escapes from the primaries are 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.

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