91-46 Berretti A., Celletti A., Chierchia L., Falcolini C.

Natural Boundaries for Area Preserving Twist Maps (35K, LaTeX) Oct 25, 91

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Abstract. We consider KAM invariant curves for generalizations of the standard map of the form $(x',y')=(x+y',y+\eps f(x))$, where $f(x)$ is an odd trigonometric polynomial. We study numerically their analytic properties by Pad\'e approximant method applied to the function which conjugates the dynamics to a rotation. In the complex $\eps$ plane, natural boundaries of different shapes are found. In the complex $\theta$ plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to $0$ as $\eps$ tends to the critical value.

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