Abstract
For near-integrable systems with two degrees of freedom, we have seen in Chapter 3 the existence of chaotic regions surrounding the separatrices associated with resonances. These regions persist for any nonzero perturbation strength ϵ, although their area tends to zero as ϵ → 0. Therefore, there is no abrupt “transition to stochasticity” at some critical ϵ, and one must define carefully the meaning of any such criterion.
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© 1992 Springer Science+Business Media New York
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Lichtenberg, A.J., Lieberman, M.A. (1992). Transition to Global Stochasticity. In: Regular and Chaotic Dynamics. Applied Mathematical Sciences, vol 38. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2184-3_4
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DOI: https://doi.org/10.1007/978-1-4757-2184-3_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3100-9
Online ISBN: 978-1-4757-2184-3
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