A lambda-lemma for partially hyperbolic tori and the obstruction property

被引：23

作者：

Cresson, J

机构：

[1] Institut de Mathematiques de Jussieu, Univ. Pierre Marie Curie, Paris V., 75252 Paris Cedex 05, Case 247

来源：

LETTERS IN MATHEMATICAL PHYSICS | 1997年 / 42卷 / 04期

关键词：

Hamiltonian systems; lambda-lemma; hyperbolic tori; topological instability;

D O I：

10.1023/A:1007433819941

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Using a scheme given by Marco, we prove that partially hyperbolic tori along resonant surfaces of near-integrable Hamiltonian systems possess the obstruction property in Arnold's terminology. The proof is based on a specific lambda lemma for these tori.

引用

页码：363 / 377

页数：15

共 10 条

[1]

Arnold V. I., 1967, PROBLEMES ERGODIQUES

[2]

ARNOLD VI, 1964, DOKL AKAD NAUK SSSR+, V156, P9

[3]

ARNOLD VI, 1992, APPL MATH SCI SERIES, V100

[4] A PROOF OF KOLMOGOROV THEOREM ON INVARIANT TORI USING CANONICAL-TRANSFORMATIONS DEFINED BY THE LIE METHOD [J].

BENETTIN, G ;

GALGANI, L ;

GIORGILLI, A ;

STRELCYN, JM .

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-GENERAL PHYSICS RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS, 1984, 79 (02) :201-223

[5] CONSERVATION OF HYPERBOLIC INVARIANT TORI FOR HAMILTONIAN SYSTEMS [J].

GRAFF, SM .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1974, 15 (01) :1-69

[6]

LOCHAK P, 1996, P NATO ADV STUD I 3

[7]

Marco JP, 1996, ANN I H POINCARE-PHY, V64, P205

[8]

Palis J., 1982, GEOMETRIC THEORY DYN

[9] THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN-SYSTEMS [J].

TRESHCHEV, DV .

MATHEMATICS OF THE USSR-SBORNIK, 1991, 68 (01) :181-203

[10]

Wiggins S., 1988, APPL MATH SCI, V73

← 1 →