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.
Titolo: | Shape of analyticity domains of Lindstedt series: the standard map |
Autori: | |
Data di pubblicazione: | 2001 |
Rivista: | |
Citazione: | 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. |
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. |
Handle: | http://hdl.handle.net/11590/137217 |
Appare nelle tipologie: | 1.1 Articolo in rivista |