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Chaos theory is a mathematical field aimed at analyzing the behavior of dynamical systems that are highly sensitive to initial conditions. A system can be totally deterministic, yet chaotic in such a sense: limits to the accuracy of knowledge of the system's exact state allow for a wide variety of outcomes. Chaos theory include calculations of limits on the length of time for which precise predictions can be made for a system, and determination of patterns evident in the subsequent chaos. Applications include meteorology, physics, engineering, economics, biology, and philosophy. In astrophysics, it can apply to orbital mechanics when more than two bodies are involved.
An example of a phenomenon considered non-chaotic (in this sense) is the shooting of a cannon, where a slight change in aim or projectile speed causes a slight change in the path of the projectile, and you can "zero in" on a target through repeated shots, making adjustments. In contrast, a pin-ball machine is considered chaotic because an extremely small change in launching the ball causes the ball's path to change dramatically after hitting a few of the obstacles, and attempting to use fine adjustments in the launch to control the ball's progress produces predictable behavior only for a very limited time-interval.