Chaos in Three-Body Dynamics: Intermittency, Strange Attractor, Kolmogorov-Sinai Entropy

Extract

The temporal structure of chaos in three-body dynamics is analyzed; the emphasis is made on a similarity and difference between three-body chaos and basic patterns of chaotic behaviour known in nonlinear physics.

1. With the use of homology mapping (Agekian and Anosova 1967), we study a set of computer models of thee-body systems in a stationary spherically symmetric potential well (Valtonen et al. (1994); the well confines the bodies, and because of this the system can generate fairly long time series. Typical time series reveal sequences of seemingly periodic motion and short bursts of strong chaos that appear in an irregular manner (Heinämäki et al. 1998). The quasi-ordered states are associated with hierarchical homology, and the quasi-period of the low-amplitude oscillations is very near the period of the temporary close binary in the system. The high-amplitude irregular states are mostly due to active three-body interplay when each of the bodies interacts with the two others with almost equal intensity. In the evolutionary history of most systems, these two extreme kinds of states alternate in an apparently random way producing together a non-stationary pattern of unpredictable behaviour.