Scaling properties for the radius of convergence of a Lindstedt series: The standard map

被引:20
作者
Berretti, A
Gentile, G
机构
[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
[2] Univ Roma 3, Dipartimento Matemat, I-00146 Rome, Italy
来源
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 1999年 / 78卷 / 02期
关键词
D O I
10.1016/S0021-7824(01)80007-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
By using a version of the tree expansion for the standard map, we prove that the radius of convergence of the corresponding Lindstedt series satisfies a scaling property as the (complex) rotation number tends to any rational (resonant) value, non-tangentially to the real axis. By suitably rescaling the perturbative parameter epsilon, the function conjugating the dynamic on the (KAM) invariant curve with given rotation number to a linear rotation has a well defined limit, which can be explicitly computed. (C) Elsevier, Paris.
引用
收藏
页码:159 / 176
页数:18
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