Asymptotic Behavior of the Domain ofAnalyticity of Invariant Curves of theStandard
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چکیده
In this contribution we study some topics of KAM theory on the so-called standard map. We consider the invariant curve of rotation number the golden mean obtained by analytical continuation, with respect the parameter ", of the invariant circle of such rotation number corresponding to the case " = 0. We show that if we consider the parameterization that conjugates the dynamics of this curve to an irrational rotation, the domain of deenition of this conjugation has a natural boundary of analyticity when " ! 0 (in the sense of the singular perturbation theory). This boundary is obtained studying the same problem for the so-called semi-standard map. To prove this result, we have used KAM-like methods adapted to the framework of the singular perturbation theory, as well matching techniques to joint diierent pieces of the conjugation, obtained studying its diierent behaviours.
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تاریخ انتشار 2007