In this paper we consider the standard map, and we study the invariant curve
obtained by analytical continuation, with respect to the perturbative parameter E,
of the invariant circle of rotation number the golden mean corresponding to the
case E=0. We show that, if we consider the parameterization that conjugates
the dynamics of this curve to an irrational rotation, the domain of definition of
this conjugation has an asymptotic boundary of analyticity when E->0 (in the
sense of the singular perturbation theory). This boundary is obtained studying the
conjugation problem for the so-called semi-standard map.
To prove this result we have used KAM-like methods adapted to the framework
of singular perturbation theory, as well as matching techniques to join di erent
pieces of the conjugation, obtained in different parts of its domain of analyticity.