The analyticity domains of the Lindstedt series for the standard map are studied numerically using Pad'e approximants to model their natural boundaries. We show that if the rotation number is a Diophantine number close to a rational value p/q, then the radius of convergence of the Lindstedt series becomes smaller than the critical threshold for the corresponding Kol’mogorov-Arnol’d-Moser curve, and the natural boundary on the plane of the complexified perturbative parameter acquires a flowerlike shape with 2q petals.

Berretti, A., Falcolini, C., & Gentile, G. (2001). Shape of analyticity domains of Lindstedt series: the standard map. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 64(1), 015101.1-015101.4 [10.1103/PhysRevE.64.015202].

Shape of analyticity domains of Lindstedt series: the standard map

FALCOLINI, Corrado;GENTILE, Guido
2001

Abstract

The analyticity domains of the Lindstedt series for the standard map are studied numerically using Pad'e approximants to model their natural boundaries. We show that if the rotation number is a Diophantine number close to a rational value p/q, then the radius of convergence of the Lindstedt series becomes smaller than the critical threshold for the corresponding Kol’mogorov-Arnol’d-Moser curve, and the natural boundary on the plane of the complexified perturbative parameter acquires a flowerlike shape with 2q petals.
Berretti, A., Falcolini, C., & Gentile, G. (2001). Shape of analyticity domains of Lindstedt series: the standard map. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 64(1), 015101.1-015101.4 [10.1103/PhysRevE.64.015202].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/137217
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