Bifurcations and monodromy of the axially symmetric 1:1:-2 resonance

被引：4

作者：

Efstathiou, Konstantinos ^{[1
]}

Hanssmann, Heinz ^{[2
]}

Marchesiello, Antonella ^{[3
]}

机构：

[1] Univ Groningen, Bernoulli Inst, POB 407, NL-9700 AK Groningen, Netherlands

[2] Univ Utrecht, Math Inst, Postbus 80010, NL-3508 TA Utrecht, Netherlands

[3] Czech Tech Univ, Fac Informat Technol, Dept Appl Math, Thakurova 9, Prague 16000 6, Czech Republic

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 146卷

关键词：

Resonance; Bifurcations; Hamiltonian monodromy; Reduction; HAMILTONIAN-SYSTEMS; PERIODIC-SOLUTIONS; EIGENVALUES; COLLISION; TORI;

D O I：

10.1016/j.geomphys.2019.103493

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from averaging along the periodic motion of the quadratic part and an imposed rotational symmetry about the vertical axis. Introducing a detuning parameter we find a rich bifurcation diagram, containing three parabolas of Hamiltonian Hopf bifurcations that join at the origin. We describe the monodromy of the resulting ramified 3-torus bundle as variation of the detuning parameter lets the system pass through 1:1:-2 resonance. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：30

共 24 条

[1]

Abraham R., 1978, Foundations of Mechanics

[2]

[Anonymous], 2007, Appl. Math. Sci

[3]

Arnold V.I., 1988, DYNAM SYST

[4]

BERTOTTI ML, 1987, B UNIONE MAT ITAL, V1B, P965

[5] BIFURCATION OF PERIODIC-SOLUTIONS NEAR A COLLISION OF EIGENVALUES OF OPPOSITE SIGNATURE [J].