Hamiltonian intermittency and Lévy flights in the three-body problem

Ivan I. Shevchenko
Phys. Rev. E 81, 066216 – Published 23 June 2010

Abstract

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 Lévy 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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  • Received 12 December 2009

DOI:https://doi.org/10.1103/PhysRevE.81.066216

©2010 American Physical Society

Authors & Affiliations

Ivan I. Shevchenko*

  • Pulkovo Observatory of the Russian Academy of Sciences, Pulkovskoje Avenue 65, St. Petersburg 196140, Russia

  • *iis@gao.spb.ru

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Vol. 81, Iss. 6 — June 2010

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