Quasi-periodic stability of normally resonant tori

被引：30

作者：

Broer, Henk W. ^{[2
]}

Ciocci, M. Cristina ^{[1
]}

Hanssmann, Heinz ^{[3
]}

Vanderbauwhede, Andre ^{[4
]}

机构：

[1] Univ Coll W Flanders, Dept PIH, B-8500 Kortrijk, Belgium

[2] Univ Groningen, Dept Math & Comp Sci, NL-9700 AK Groningen, Netherlands

[3] Univ Utrecht, Inst Math, NL-3508 TA Utrecht, Netherlands

[4] Univ Ghent, Dept Pure Math & Comp Algebra, B-9000 Ghent, Belgium

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2009年 / 238卷 / 03期

关键词：

Kolmogorov-Arnold-Moser theory; Quasi-periodic stability; Normal-internal resonance; Covering space; Preservation of structure; Reversibility; Equivariance; HOPF-BIFURCATION; DIMENSIONAL TORI; SYSTEMS; PERSISTENCE;

D O I：

10.1016/j.physd.2008.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：309 / 318

页数：10

共 28 条

[1]

[Anonymous], DYN REPORT

[2]

Arnold V. I., 1971, Russian Math. Surveys, V26, P29

[3]

Bourgain J, 1997, MATH RES LETT, V4, P445

[4]

BRAAKSMA BLJ, 1990, MEM AM MATH SOC, V83, P83

[5] ON A QUASI-PERIODIC HOPF-BIFURCATION [J].

BRAAKSMA, BLJ ;

BROER, HW .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1987, 4 (02) :115-168

[6] Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach [J].

Broer, H ;

Hanssmann, H ;

Jorba, A ;

Villanueva, J ;

Wagener, F .

NONLINEARITY, 2003, 16 (05) :1751-1791

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

Broer, H. W. ;

Hoo, J. ;

Naudot, V. .

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

[8] The quasi-periodic reversible Hopf bifurcation [J].

Broer, Henk W. ;

Ciocci, M. Cristina ;

Hanssmann, Heinz .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (08) :2605-2623

[9] The quasi-periodic Hamiltonian Hopf bifurcation [J].

Broer, Henk W. ;

Hanssmann, Heinz ;

Hoo, Jun .

NONLINEARITY, 2007, 20 (02) :417-460

[10]

BROER HW, 1995, J DYNAM DIFFERENTIAL, V7, P191, DOI DOI 10.1007/BF02218818

← 1 2 3 →