Hamiltonian intermittency and L\'evy flights in the three-body problem

TL;DR

This paper investigates the statistical behavior of disruption and chaos times in a hierarchical three-body system, revealing Levy flights and heavy-tailed decay in survival probabilities, with implications for resonant scattering.

Contribution

It demonstrates the presence of Levy flights and heavy-tailed distributions in the disruption dynamics of the three-body problem, providing new insights into orbital chaos and stability.

Findings

Orbital periods and orbit sizes exhibit Levy flights at disruption edge.

Survival probability decays with a heavy tail, power-law index -2/3.

Lyapunov and disruption times are quasilinearly related.

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 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.