A New KAM Iteration with Nearly Infinitely Small Steps in Reversible Systems of Polynomial Character

被引：3

作者：

Zhang, Dongfeng ^{[1
]}

Xu, Junxiang ^{[1
]}

Wang, Xiaocai ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Jiangsu, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2018年 / 17卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Invariant tori; Reversible systems; Brjuno-Russmann's non-resonant condition; Small divisors; KAM iteration; NON-DEGENERACY CONDITION; LOWER-DIMENSIONAL TORI; INTEGRABLE HAMILTONIAN-SYSTEMS; INVARIANT TORI; GEVREY-SMOOTHNESS; CONTEXT; PERSISTENCE; STABILITY;

D O I：

10.1007/s12346-017-0229-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the persistence of invariant tori of analytic reversible systems under Brjuno-Russmann's non-resonant condition by an improved KAM iteration, but the frequency may undergo some drift. Furthermore, if the frequency mapping has nonzero Brouwer's topological degree, then the invariant torus with prescribed frequency can persist. In the proof we propose a new method of KAM iteration for reversible systems, containing an artificial parameter q, 0 < q < 1, which makes the steps of KAM iteration infinitely small in the speed of the function q(n)epsilon rather than super exponential function epsilon(lambda n), 1 < lambda < 2.

引用

页码：271 / 289

页数：19

共 4 条

[1] A New KAM Iteration with Nearly Infinitely Small Steps in Reversible Systems of Polynomial Character
Dongfeng Zhang
Junxiang Xu
Xiaocai Wang
Qualitative Theory of Dynamical Systems, 2018, 17 : 271 - 289
[2] KAM ITERATION WITH NEARLY INFINITELY SMALL STEPS IN DYNAMICAL SYSTEMS OF POLYNOMIAL CHARACTER
Ruessmann, Helmut
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (04): : 683 - 718
[3] A New KAM Theorem for the Hyperbolic Lower Dimensional Tori in Reversible Systems
Wang, Xiaocai
Xu, Junxiang
Zhang, Dongfeng
ACTA APPLICANDAE MATHEMATICAE, 2016, 143 (01) : 45 - 61
[4] A New KAM Theorem for the Hyperbolic Lower Dimensional Tori in Reversible Systems
Xiaocai Wang
Junxiang Xu
Dongfeng Zhang
Acta Applicandae Mathematicae, 2016, 143 : 45 - 61

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