Shadowing unstable orbits of the Sitnikov elliptic 3-body problem

Details Shadowing unstable orbits of the Sitnikov elliptic 3-body problem Shadowing unstable orbits of the Sitnikov elliptic 3-body problem

2010-05-07

arxiv.org/abs/1005.1225v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

9 pages, 13 figures, accepted in MNRAS

Scientific paper

Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative of true dynamics. Using the Sitnikov Problem as an example, it is demonstrated that unstable orbits of the 3-body problem can be shadowed for long periods of time. In addition, it is shown that the stretching of phase space near escape and capture regions is a cause for the failure of the shadowing refinement procedure.

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