Abstract
Chaotic behavior in a dynamical system is most easily understood as a breakdown of the invariant tori due to the perturbations. The KAM theorem deals with this process of disintegration and shows that it is gradual. The resulting situation in phase space, to be called soft chaos, is smooth wherever the tori are intact, but it has many rough spots that are associated with resonances or phase-locking. This phenomenon happens when two degrees of freedom get stuck with the ratio of their frequencies given by a rational number. Soft chaos can be explained by estimating the size of the domain of phase space where phase-lock occurs as a function of the perturbation strength.
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© 1990 Springer Science+Business Media New York
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Gutzwiller, M.C. (1990). Soft Chaos and the KAM Theorem. In: Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0983-6_10
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DOI: https://doi.org/10.1007/978-1-4612-0983-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6970-0
Online ISBN: 978-1-4612-0983-6
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