 98689 Alberto Berretti, Guido Gentile
 Bryuno Function and the Standard Map
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Oct 30, 98

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Abstract. For the standard map the homotopically nontrivial 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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