Scaling law in the standard map critical function. Interpolating Hamiltonian and frequency map analysis

Timoteo Carletti, Jacques Laskar

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    Abstract

    We study the behaviour of the standard map critical function in a neighbourhood of a fixed resonance, that is the scaling law at the fixed resonance. We prove that for the fundamental resonance the scaling law is linear. We show numerical evidence that for the other resonances p/q, q>1, p \neq 0 and p and q relatively prime, the scaling law follows a power-law with exponent 1/q.
    Original languageEnglish
    Pages (from-to)2033-2061
    Number of pages29
    JournalNonlinearity
    Volume13
    Publication statusPublished - 2000

    Keywords

    • Bruno number
    • Critical function
    • Frequency map analysis
    • standard map

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