Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition

被引：0

作者：

Dong Feng Zhang

Jun Xiang Xu

机构：

[1] Southeast University,Department of Mathematics

来源：

Acta Mathematica Sinica, English Series | 2008年 / 24卷

关键词：

hyperbolic invariant tori; KAM iteration; Gevrey-smooth; non-degeneracy condition; 70H08; 37J40; 34C27;

D O I：

暂无

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学科分类号：

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 Rüssmann’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

共 15 条

[1] Invariant Hyperbolic Tori for Gevrey-smooth Hamiltonian Systems Under Russmann's Non-degeneracy Condition
Zhang, Dong Feng
Xu, Jun Xiang
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2008, 24 (10) : 1625 - 1636
[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 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
[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 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
[7] 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
[8] On invariant tori of vector field under weaker non-degeneracy condition
Zhang, Dongfeng
Xu, Junxiang
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (05): : 1381 - 1394
[9] 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
[10] 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

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