Persistence of hyperbolic-type degenerate invariant tori with prescribed frequencies in reversible systems

被引：0

作者：

Qu, Ru ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

来源：

NONLINEARITY | 2025年 / 38卷 / 01期

关键词：

reversible systems; KAM iteration; degenerate lower-dimensional tori; degenerate equilibrium points; STABILITY;

D O I：

10.1088/1361-6544/ad9b1c

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we focus on the persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in reversible systems. The proof is based on the stability analysis of minimal points of real analytic functions and the non-degeneracy brought by higher-order terms.

引用

页数：26

共 15 条

[1] Normal linear stability of quasi-periodic tori [J].

Broer, H. W. ;

Hoo, J. ;

Naudot, V. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 232 (02) :355-418

[2] Quasi-periodic stability of normally resonant tori [J].

Broer, Henk W. ;

Ciocci, M. Cristina ;

Hanssmann, Heinz ;

Vanderbauwhede, Andre .

PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (03) :309-318

[3]

Eliasson L., 1988, Annali della Scuola Normale Superiore di Pisa, V15, P115

[4] DEGENERATE LOWER DIMENSIONAL INVARIANT TORT IN REVERSIBLE SYSTEM [J].

Hu, Shengqing ;

Liu, Bin .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (08) :3735-3763

[5] COMPLETELY DEGENERATE LOWER-DIMENSIONAL INVARIANT TORI IN REVERSIBLE SYSTEMS [J].

Jing, Tianqi ;

Si, Wen .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (10) :4247-4260

[6] On lower dimensional invariant tori in reversible systems [J].

Liu, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 176 (01) :158-194

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

MOSER, J .

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

[8]

Sevryuk M B., 1986, Reversible Systems (Lecture Notes in Mathematics), DOI [10.1007/bfb0075877, DOI 10.1007/BFB0075877]

[9] Partial preservation of frequencies in KAM theory [J].

Sevryuk, MB .

NONLINEARITY, 2006, 19 (05) :1099-1140

[10] THE ITERATION-APPROXIMATION DECOUPLING IN THE REVERSIBLE KAM THEORY [J].

SEVRYUK, MB .

CHAOS, 1995, 5 (03) :552-565

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