Destruction Of Lagrangian Torus For Positive Definite Hamiltonian Systems

被引：17

作者：

Cheng, Chong-Qing ^{[1
]}

Wang, Lin ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2013年 / 23卷 / 03期

关键词：

Lagrangian torus; nearly integrable Hamiltonian system; action minimizing orbit; INVARIANT CIRCLES; CURVES; DIFFEOMORPHISMS; THEOREM; RING;

D O I：

10.1007/s00039-013-0213-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an integrable Hamiltonian , we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily -small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under -small perturbations by Poschel (Comm Pure Appl Math 35:653-696, 1982).

引用

页码：848 / 866

页数：19

共 50 条

[1] Destruction Of Lagrangian Torus For Positive Definite Hamiltonian Systems
Chong-Qing Cheng
Lin Wang
[J]. Geometric and Functional Analysis, 2013, 23 : 848 - 866
[2] Homoclinic orbits of positive definite Lagrangian systems
Zheng, Yong
Cheng, Chong-Qing
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 229 (01) : 297 - 316
[3] Strictly Positive Definite Kernels on the Torus
Guella, J.
Menegatto, V. A.
[J]. CONSTRUCTIVE APPROXIMATION, 2017, 46 (02) : 271 - 284
[4] Strictly Positive Definite Kernels on the Torus
J. Guella
V. A. Menegatto
[J]. Constructive Approximation, 2017, 46 : 271 - 284
[5] FRACTIONAL HAMILTONIAN SYSTEMS WITH POSITIVE SEMI-DEFINITE MATRIX
Torres, Cesar
Zhang, Ziheng
Mendez, Amado
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (06): : 2436 - 2453
[6] ACTION MINIMIZING INVARIANT-MEASURES FOR POSITIVE DEFINITE LAGRANGIAN SYSTEMS
MATHER, JN
[J]. MATHEMATISCHE ZEITSCHRIFT, 1991, 207 (02) : 169 - 207
[7] THE INDEX THEORY FOR A CLASS OF HAMILTONIAN-SYSTEMS NON POSITIVE DEFINITE
DONOFRIO, B
EKELAND, I
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1987, 305 (06): : 249 - 251
[8] Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
Jing Chen
Yuzhen Bai
[J]. Science in China Series A: Mathematics, 2006, 49 : 1864 - 1866
[9] Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
CHEN Jing & BAI Yuzhen Department of Mathematics
Department of Mathematics
[J]. Science China Mathematics, 2006, (12) : 1864 - 1866
[10] Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
Chen Jing
Bai Yuzhen
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (12): : 1864 - 1866

← 1 2 3 4 5 →