Hamiltonian intermittency and Lévy flights in the three-body problem

Details Hamiltonian intermittency and Lévy flights in the three-body problem Hamiltonian intermittency and Lévy flights in the three-body problem

2009-07-10

arxiv.org/abs/0907.1773v4

Phys. Rev. E, 81, 066216 (2010) (http://pre.aps.org/toc/PRE/v81/i6)

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

34 pages, including 9 figures

Scientific paper

10.1103/PhysRevE.81.066216

We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit L\'evy flights. Due to them, the time decay of the survival probability is heavy-tailed with the power-law index equal to -2/3, while the relation between the Lyapunov and disruption times is quasilinear. Applicability of these results in an "hierarchical resonant scattering" setting for a three-body interaction is discussed.

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