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Analytic and numerical tools for the study of quasi-periodic motions in hamiltonian systems.

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Figure

Figure II.1: Schematic representation of the recurrent computations performed to evaluate Ddµ(f(z)).
Figure II.2: Devil’s Staircaseε α �→ ρ(fα) (top-left) and its derivative (top-right) for the Arnold family with = 0.75
Figure II.3:√Right: error (estimated using (II.13)) in �→rotation number Left: Graph of the derivatives ε Dαρ(α(ε), ε) and ε �→ Dερ(α(ε), ε) along Tθ, for the fixed θ = (5 − 1)/2
Table II.1: Derivatives of 2πα(ε) at the origin for θ = (√5 − 1)/2. The column e1 corresponds to the estimatederror using (II.13)
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