Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Russmann's non-degeneracy condition

被引：13

作者：

Zhang, Dongfeng ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 323卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hamiltonian systems; KAM iteration; Gevrey-smoothness;

D O I：

10.1016/j.jmaa.2005.10.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove Gevrey-smoothness of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under Russmann's non-degeneracy condition by an improved KAM iteration. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：293 / 312

页数：20

共 19 条

[1] WHITNEY EXTENSION THEOREM FOR NONQUASIANALYTIC CLASSES OF ULTRADIFFERENTIABLE FUNCTIONS [J].

BONET, J ;

BRAUN, RW ;

MEISE, R ;

TAYLOR, BA .

STUDIA MATHEMATICA, 1991, 99 (02) :155-184

[2] Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach [J].

Broer, H ;

Hanssmann, H ;

Jorba, A ;

Villanueva, J ;

Wagener, F .

NONLINEARITY, 2003, 16 (05) :1751-1791

[3]

BROER H, 1996, LECT NOTES MATH, V1645

[4]

BRUNA J, 1980, J LOND MATH SOC, V22, P495

[5]

Eliasson L. H., 1988, ANN SC NORM SUPER S, V15, P115

[6] ON THE LEBESGUE MEASURE OF THE PERIODIC POINTS OF A CONTACT MANIFOLD [J].

PETKOV, V ;

POPOV, G .

MATHEMATISCHE ZEITSCHRIFT, 1995, 218 (01) :91-102

[7] Invariant tori, effective stability, and quasimodes with exponentially small error terms I - Birkhoff normal forms [J].

Popov, G .

ANNALES HENRI POINCARE, 2000, 1 (02) :223-248

[8] KAM theorem for Gevrey Hamiltonians [J].

Popov, G .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2004, 24 :1753-1786

[9] ON ELLIPTIC LOWER DIMENSIONAL TORI IN HAMILTONIAN-SYSTEMS [J].

POSCHEL, J .

MATHEMATISCHE ZEITSCHRIFT, 1989, 202 (04) :559-608

[10] INTEGRABILITY OF HAMILTONIAN-SYSTEMS ON CANTOR SETS [J].

POSCHEL, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (05) :653-696

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