Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.1, pp.64-67

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 1, pp.64-67

Characterization of the Incoming Asymptotes in the Restricted Three-Body Problem.
L. Benet and T.H. Seligman

We consider the subset of initial conditions, which result in trapped orbits for the circular Restricted Three-Body Problem as a function of the Jacobi integral, in the case of equal masses of the heavy bodies. We show that this set contributes in localizing the major bifurcations of the problem where the chaotic saddle changes abruptly, while it is not sufficient to distinguish between the hyperbolic or non-hyperbolic character of the chaotic saddle in finite precision measurements.

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