Abstract
Regular motion often appears to be less symmetric than chaotic motion. For the case of Hamiltonian systems, the reduced symmetry of bounded regular motion can be derived from the structure of the phase space orbit. The symmetry restrictions do not apply when the motion is chaotic, so higher symmetry is possible for chaotic motion. Numerical experiments clearly show symmetry for chaos which is not allowed for regular motion. The symmetry differences between regular and chaotic motion can be used to identify chaos.
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