The Ilya Prigogine Center for Studies in
Statistical Mechanics and Complex Systems
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One of the most widely-studied systems that can display complex behavior is the simultaneous collision, or scattering, of three objects. For simplicity's sake, it is easy to think of the objects as hard-shelled billiard balls, as in the diagram here.
The reason that this system displays complex behavior is that, in contrast to the scattering of only two bodies, it is not possible to use the initial conditions of the three-body system to calculate the conditions at a later time to infinite precision.

Although the mathematical theory of this system remains incomplete, in recent years, researchers at the Center for Statistical Mechanics have made tremendous strides in the understanding of this system.

Text and Graphics (c) 1999 by Matthew Trump. Original three-panel diagrams by T. Miyasaka