Hamiltonian intermittency and Lévy flights in the three-body problem
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.
- 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;
- Low-dimensional 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
- E-Print:
- 34 pages, including 9 figures