PERSISTENCE OF DEGENERATE HYPERBOLIC LOWER-DIMENSIONAL INVARIANT TORI IN HAMILTONIAN SYSTEMS WITH BRUNO'S CONDITIONS

被引：0

作者：

Yang, Xiaomei ^{[1
]}

Xu, Junxiang ^{[2
]}

机构：

[1] Jinling Inst Technol, Coll Sci, Nanjing 211169, Peoples R China

[2] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Hamiltonian system; KAM iteration; non-degeneracy condition; de-generate equilibrium point; RESPONSE SOLUTIONS; BIFURCATIONS;

D O I：

10.1090/proc/16184

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proves the persistence of degenerate hyperbolic lower dimensional invariant tori in Hamiltonian systems with Bruno non-degeneracy conditions, whose frequency vector is a small dilation of the prescribed one. The proof is based on the stability of real roots of approximating real odd-order polynomials.

引用

页码：2435 / 2447

页数：13

共 50 条

[21] Persistence of lower dimensional invariant tori in a class of reversible systems
Hong, Weiwei
Zhang, Dongfeng
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2018, 33 (01): : 72 - 92
[22] Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems
Yang, Xiaomei
Xu, Junxiang
Jiang, Shunjun
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2023, 35 (01) : 329 - 354
[23] Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems
Xiaomei Yang
Junxiang Xu
Shunjun Jiang
Journal of Dynamics and Differential Equations, 2023, 35 : 329 - 354
[24] ON THE PERSISTENCE OF LOWER-DIMENSIONAL TORI IN REVERSIBLE SYSTEMS WITH HIGH DIMENSIONAL DEGENERATE EQUILIBRIUM UNDER SMALL PERTURBATIONS
Wang, Xiaocai
Cao, Xiaofei
Liu, Xuqing
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (11): : 6441 - 6463
[25] Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems
Liu, ZX
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (08) : 1319 - 1342
[26] The persistence of elliptic lower dimensional tori with prescribed frequency for Hamiltonian systems
Lu, Xuezhu
Xu, Junxiang
Kong, Yuedong
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2015, (10) : 1 - 12
[27] A KAM Theorem for Hyperbolic-Type Degenerate Lower Dimensional Tori in Hamiltonian Systems
Jiangong You
Communications in Mathematical Physics, 1998, 192 : 145 - 168
[28] Persistence of hyperbolic tori in Hamiltonian systems
Li, Y
Yi, YF
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 208 (02) : 344 - 387
[29] 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
[30] Invariant hyperbolic tori for Hamiltonian systems with Russmann nondegeneracy conditions
Cong, FZ
Li, Y
Jin, DJ
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (03) : 831 - 851

← 1 2 3 4 5 →