Asymptotic Behaviour of the Domain of Analyticity of Invariant Curves of the Standard Map

In this paper we consider the standard map and we study the invariant curve obtained by analytical continuation with respect to the perturbative parameter of the invariant circle of rotation number the golden mean corresponding to the case We show that if we consider the parameterization that conjugates the dynamics of this curve to an irrational rotation the domain of de nition of this conjugation has an asymptotic boundary of analyticity when 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 di erent parts of its domain of analyticity