ON THE EXISTENCE OF INVARIANT TORI IN NON-CONSERVATIVE DYNAMICAL SYSTEMS WITH DEGENERACY AND FINITE DIFFERENTIABILITY

被引：8
作者：
Li, Xuemei [1 ]
Shang, Zaijiu [2 ]
机构：
[1] Hunan Normal Univ, Dept Math, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Chinese Acad Sci, HLM,Acad Math & Syst Sci, Beijing 100190, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 07期
关键词：
Invariant torus; small frequency; degeneracy; finite differentiability; LOWER-DIMENSIONAL TORI; HAMILTONIAN-SYSTEMS; THEOREM;
D O I：
10.3934/dcds.2019171
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish a KAM-theorem about the existence of invariant tori in non-conservative dynamical systems with finitely differentiable vector fields and multiple degeneracies under the assumption that the integrable part is finitely differentiable with respect to parameters, instead of the usual assumption of analyticity. We prove these results by constructing approximation and inverse approximation lemmas in which all functions are finitely differentiable in parameters.
引用
收藏
页码：4225 / 4257
页数：33
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