- 91-46 Berretti A., Celletti A., Chierchia L., Falcolini C.
- Natural Boundaries for Area Preserving Twist Maps
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.