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For a typical Hamiltonian system, the classical phase space displays a hierarchical mixture of integrable and chaotic components down to smaller and smaller scales. As a consequence, the probability of Poincaré recurrences to the same region, or the survival probability up to time t inside a given region decays algebraically as P(t) ∝ t−α, with α ≈ 1.5−3.
© 2000 IEEE
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