Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems ?

被引：4

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：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 346卷

基金：

中国国家自然科学基金;

关键词：

Reversible system; KAM iteration; Degenerate equilibrium point; Lower dimensional invariant tori; RESPONSE SOLUTIONS;

D O I：

10.1016/j.jde.2022.11.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the persistence of multi-dimensional degenerate hyperbolic lower dimensional in-variant tori with prescribed frequencies in reversible systems. The proof is based on some KAM techniques and the topological degree theory. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：229 / 253

页数：25

共 30 条

[1]

[Anonymous], 2001, Proceedings of Symposia in Pure Mathematics

[2]

[Anonymous], 1990, J. Sov. Math, DOI DOI 10.1007/BF01094996

[3]

[Anonymous], J DYNAM DIFFERENTIAL

[4]

Deimling K., 1985, Nonlinear Functional Analysis, DOI [10.1007/978-3-662-00547-7, DOI 10.1007/978-3-662-00547-7]

[5] ON THE NUMBER OF SOLUTIONS TO POLYNOMIAL SYSTEMS OF EQUATIONS [J].

GARCIA, CB ;

LI, TY .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (04) :540-546

[6] Degenerate lower-dimensional tori under the Bryuno condition [J].

Gentile, Guido .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 :427-457

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

GRAFF, SM .

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

[8] Parabolic invariant tori in quasi-periodically forced skew-product maps [J].

Guan, Xinyu ;

Si, Jianguo ;

Si, Wen .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 277 :234-274

[9] Degenerate lower-dimensional tori in Hamiltonian systems [J].

Han, Yuecai ;

Li, Yong ;

Yi, Yingfei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (02) :670-691

[10] Completely degenerate lower-dimensional invariant tori for Hamiltonian system [J].

Hu, Shengqing ;

Liu, Bin .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (11) :7459-7480

← 1 2 3 →