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ABSTRACT  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 three‐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.

Shadowing unstable orbits of the Sitnikov elliptic three‐body problem