Relativistic effects in the chaotic Sitnikov problem

TL;DR

This paper explores how relativistic effects influence the chaotic dynamics of the Sitnikov problem, revealing bifurcations, transient chaos, and the structure of chaotic saddles as the gravitational radius varies.

Contribution

It provides the first detailed analysis of relativistic effects on the phase space structure and chaos in the Sitnikov problem using the first post-Newtonian approximation.

Findings

Phase space structure depends strongly on gravitational radius

Bifurcations occur with increasing relativistic effects

Transient chaos and chaotic saddle properties vary with gravitational radius

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 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.