A Dynamical System is chaotic if it

- 1. Has a Dense collection of points with periodic orbits,
- 2. Is sensitive to the initial condition of the system (so that initially nearby points can evolve quickly into very different states), and
- 3. Is Topologically Transitive.

An example of a simple physical system which displays chaotic behavior is the motion of a magnetic pendulum over a plane containing two or more attractive magnets. The magnet over which the pendulum ultimately comes to rest (due to frictional damping) is highly dependent on the starting position and velocity of the pendulum (Dickau). Another such system is a double pendulum (a pendulum with another pendulum attached to its end).

**References**

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1999-05-26