PERSISTENCE OF THE NON-TWIST TORUS IN NEARLY INTEGRABLE HAMILTONIAN SYSTEMS

被引：23

作者：

Xu, Junxiang ^{[1
]}

You, Jiangong ^{[2
]}

机构：

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

[2] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Hamiltonian system; KAM iteration; invariant tori; non-degeneracy condition; INVARIANT TORI; DEGENERACY; SETS;

D O I：

10.1090/S0002-9939-10-10151-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider analytic nearly integrable hamiltonian systems, and prove that if the frequency mapping has nonzero Brouwer topo-logical degree at some Diophantine frequency, then the invariant torus with this frequency persists under small perturbations.

引用

页码：2385 / 2395

页数：11

共 16 条

[1]

Arnold V.I., 1963, Russ. Math. Surv., V18, P9, DOI DOI 10.1070/RM1963V018N05ABEH004130

[2]

ARNOLD VI, 1988, ENCY MATH SCI, V3

[3] Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems [J].

Cheng, CQ .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1996, 177 (03) :529-559

[4]

Eliasson L H., 1988, Ann. della Scuola Norm. Super. Pisa-Cl. Sci, V15, P115

[5]

Kolmogorov A.N., 1954, Dokl. Akad. Nauk SSSR, V98, P527, DOI DOI 10.1007/BFB0021737

[6] CONVERGENT SERIES EXPANSIONS FOR QUASI-PERIODIC MOTIONS [J].

MOSER, J .

MATHEMATISCHE ANNALEN, 1967, 169 (01) :136-&

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

POSCHEL, J .

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

[8]

POSCHEL J, 1992, COMMUNICATION MAY

[9] INVARIANT TORI IN NON-DEGENERATE NEARLY INTEGRABLE HAMILTONIAN SYSTEMS [J].

Ruessmann, H. .

REGULAR & CHAOTIC DYNAMICS, 2001, 6 (02) :119-204

[10]

Russmann H., 1990, MATH APPL, V59, P211

← 1 2 →