Chaos in the 3-body Problem

The three-body problem exhibits all of the hallmarks of chaos. In particular, the outcome of any given interaction depends sensitively on the initial conditions. The following image shows how the final state of a scattering encounter between a binary star system and another star depends on the initial phase (horizontal axis) of the binary and the impact parameter (vertical axis) of the incomer. Color represents the angle at which the star that eventually escapes leave the interaction region. Note the alternating regions of regular (smooth) and irregular (chaotic, resonant) behavior.

Each pixel in this image coresponds to a complete three-body encounter. The particular series of calculations shown here has relative velocity at infinity equal to 10% of the binary orbit speed. Encounters such as these are believed to be important in determining the dynamical evolution of globular star clusters in the Milky Way galaxy.

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