Theory and applications of Fast Lyapunov Indicators for the computation of transit orbits in the three-body problem

Description

In the last decades finite time chaos indicators have been used to compute the phase-portraits of complex dynamics as well as the center, stable and unstable manifolds originating at the partially hyperbolic equilibria, and the Lagrangian Coherent Structures of aperiodic flows. While the definition of most chaos indicators is clearly inspired by the Characteristic Lyapunov Exponent theory, their use is oriented to extract all the information which is contained in the solutions of the variational equations in short time intervals. We here review through examples why the computation of short time chaos indicators is particularly powerful for those systems whose solutions may have an asymptotic behaviour very different from the short-term one, as it can be the case of sequences of close encounters in gravitational systems and the advection of particles in aperiodic flows. The main case study here considered is the computation of transit orbits in the restricted three-body problem.

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