91-46 Berretti A., Celletti A., Chierchia L., Falcolini C.
Natural Boundaries for Area Preserving Twist Maps (35K, LaTeX) Oct 25, 91
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 91-46.src( desc , 91-46.tex )