Hamiltonian intermittency and Lévy flights in the threebody problem
Abstract
We consider statistics of the disruption and Lyapunov times in an hierarchical restricted threebody 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 heavytailed with the powerlaw 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 threebody interaction is discussed.
 Publication:

Physical Review E
 Pub Date:
 June 2010
 DOI:
 10.1103/PhysRevE.81.066216
 arXiv:
 arXiv:0907.1773
 Bibcode:
 2010PhRvE..81f6216S
 Keywords:

 05.45.Ac;
 05.45.Pq;
 45.05.+x;
 Lowdimensional chaos;
 Numerical simulations of chaotic systems;
 General theory of classical mechanics of discrete systems;
 Astrophysics  Earth and Planetary Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  General Physics
 EPrint:
 34 pages, including 9 figures