Transition to Global Stochasticity
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.
KeywordsRotation Number Primary Resonance Standard Mapping Continue Fraction Expansion Island Chain
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