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 ∈, although their area tends to zero as ∈ → 0. Therefore, there is no abrupt “transition to stochasticity” at some critical ∈, 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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