98-689 Alberto Berretti, Guido Gentile

Bryuno Function and the Standard Map (119K, LaTeX2e) Oct 30, 98

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

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