Invariant Hyperbolic Tori for Gevrey-smooth Hamiltonian Systems Under Russmann's Non-degeneracy Condition

被引：1

作者：

Zhang, Dong Feng ^{[1
]}

Xu, Jun Xiang ^{[1
]}

机构：

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

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 10期

关键词：

hyperbolic invariant tori; KAM iteration; Gevrey-smooth; non-degeneracy condition;

D O I：

10.1007/s10114-008-6180-x

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 hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Russmann's non-degeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth, with the same Gevrey index as the Hamiltonian.

引用

页码：1625 / 1636

页数：12

共 16 条

[1] Invariant tori for Gevrey-smooth Hamiltonian systems under Russmann's non-degeneracy condition
Zhang, Dongfeng
Xu, Junxiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (07) : 2240 - 2257
[2] Invariant Hyperbolic Tori for Gevrey-smooth Hamiltonian Systems Under Rfissmann's Non-degeneracy Condition
Dong Feng ZHANG Jun Xiang XU Department of Mathematics
Acta Mathematica Sinica,English Series, 2008, (10) : 1625 - 1636
[3] Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition
Dong Feng Zhang
Jun Xiang Xu
Acta Mathematica Sinica, English Series, 2008, 24
[4] On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Russmann's non-degeneracy condition
Zhang, Dongfeng
Xu, Junxiang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2006, 16 (03) : 635 - 655
[5] Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Russmann's non-degeneracy condition
Xu, Junxiang
You, Jiangong
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 235 (02) : 609 - 622
[6] GEVREY-SMOOTHNESS OF INVARIANT TORI FOR ANALYTIC REVERSIBLE SYSTEMS UNDER RUSSMANN'S NON-DEGENERACY CONDITION
Wang, Xiaocai
Xu, Junxiang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (02) : 701 - 718
[7] Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Russmann's non-degeneracy condition
Zhang, Dongfeng
Xu, Junxiang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) : 293 - 312
[8] On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Russmann's non-degeneracy condition
Wang, Shaoping
Zhang, Dongfeng
Xu, Junxiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (08) : 1675 - 1685
[9] Invariant hyperbolic tori for Hamiltonian systems with Russmann nondegeneracy conditions
Cong, FZ
Li, Y
Jin, DJ
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (03) : 831 - 851
[10] On invariant tori of vector field under weaker non-degeneracy condition
Dongfeng Zhang
Junxiang Xu
Nonlinear Differential Equations and Applications NoDEA, 2015, 22 : 1381 - 1394

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