A comparison is made of two transformation theories which can be used in classical mechanics: the averaging method as generalized by Kruskal and the superoperator transformation theory used in statistical mechanics by Prigogine et al. For the class of systems considered, a striking connection is found which, on the one hand, illustrates some of the general features of the superoperator method and, on the other, provides an interesting method for calculating invariants of nearly periodic systems. This latter method is shown to be equivalent to, but more systematic than, that developed by McNamara and Whiteman.
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I. Prigogine, Topics in Non‐Linear Physics, Proceedings of International School of Non‐Linear Math. and Phys. Munich 1966 (Springer, New York, 1968).
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V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
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© 1973 The American Institute of Physics.
1973
The American Institute of Physics
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