Intermittent chaos in three-body dynamics

Abstract

Chaotic behaviour of dynamical three-body systems is characterized by the fact that their evolution consists typically of sequences of transient states that change from one to another in an unpredictable manner. Some of these states are fairly regular ones; for instance, a hierarchical state with a very close binary and a remote third body. Other ones are more chaotic; for instance, a state of interplay in which each body interacts with two others with more or less equal intensity. The alternation of these states is similar to the phenomenon of intermittency discovered first in the ocean flows, where laminar currents alternate with areas of developed turbulence. Onset of chaos and the structure of intermittency in the dynamics of three-body systems is the focus of the present paper. General physical considerations on the nature of chaos in nonlinear systems are applied to the analysis of the three-body dynamics given by analytical and computer models. Onset of chaos and the nature of unpredictability in a typical elementary act of three-body interaction is studied with analytical methods. High sensitivity of the systems to small changes in control parameters is also demonstrated and a critical mass for transition to chaos is found. Computer simulations and homology mapping are used to clarify why and how the three-body systems are sensitive to fine details of initial conditions. Physical characteristics of local dynamical instability, which is the fundamental mechanism of the onset of chaos in dynamical systems, are estimated. Rapid divergence of two initially close trajectories in phase space is demonstrated. Stochasization in an ensemble of systems is studied with the use of homology mapping. A strange attractor with fractal dimension slightly above 2 is discovered in the long time series generated by the system in the state of intermittent chaos. General manifestations of weak low-dimensional intermittent chaos in three-body dynamics are finally summarized.