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For the standard map the homotopically non-trivial invariant curves of rotation number ω satisfying the Bryuno condition are shown to be analytic in the perturbative parameter ε, provided |ε| is small enough. The radius of convergence ρ(ω) of the Lindstedt series -sometimes called critical function of the standard map -is studied and the relation with the Bryuno function B(ω) is derived: the quantity | log ρ(ω) + 2B(ω)| is proved to be bounded uniformily in ω. cleare, Sez. Tor Vergata

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