Bryuno function and the standard map

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) + 2B(omega)/ is proved to be bounded uniformly in omega.