Gevrey Smoothness of Families of Invariant Curves for Analytic Area Preserving Mappings

被引：0
|
作者：
Zhang, Dongfeng [1 ]
Xu, Junxiang [1 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2018年 / 154卷 / 01期
关键词：
Invariant curve; Area preserving mapping; Gevrey index; KAM iteration; NON-DEGENERACY CONDITION; HAMILTONIAN-SYSTEMS; EXTENSION THEOREM; TWIST MAPPINGS; KAM THEORY; TORI; STABILITY;
D O I：
10.1007/s10440-017-0131-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we prove the existence of a Gevrey family of invariant curves for analytic area preserving mappings. The Gevrey smoothness is expressed by Gevrey index. We specifically obtain the Gevrey index of families of invariant curves which is related to the smoothness of area preserving mappings and the exponent of small divisors condition. Moreover, we obtain a Gevrey normal form of area preserving mappings in a neighborhood of the union of the invariant curves.
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页码：31 / 42
页数：12
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