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 curv e obtained by analytical continuation, with respect to the perturbative par ameter epsilon, of the invariant circle of rotation number equal to the gol den mean, corresponding to the case epsilon = 0. We show that, if we consid er the parametrization that conjugates the dynamics of this curve to an irr ational rotation, the domain of definition of this conjugation has an asymp totic boundary of analyticity when epsilon --> 0 (in the sense of the singu lar perturbation theory). This boundary is obtained by studying the conjuga tion 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 fferent pieces of the conjugation, obtained in different parts of its domai n of analyticity. AMS classification scheme numbers: 30B40, 34C50, 39A10, 3 9B32, 40A05, 41A58.