THE LISSAJOUS TRANSFORMATION III. PARAMETRIC BIFURCATIONS

被引：25

作者：

Miller, Bruce R. ^{[1
]}

机构：

[1] NIST, Gaithersburg, MD 20899 USA

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 1991年 / 51卷 / 03期

关键词：

Bifurcations; elliptic oscillator; integrability; Lissajous transformation; normalization; symmetry;

D O I：

10.1007/BF00051693

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We examine a parametric family of cubic perturbed 1-1 resonant harmonic oscillators with an aim to understanding the phase flows of the reduced system. Variation of the parameters leads the system through five bifurcations of different types. Some bifurcations are due to passage through cases of discrete symmetry or integrability. A conjecture correlating degenerate equilibria in reduced systems with integrability is modified and reinforced.

引用

页码：251 / 270

页数：20

共 17 条

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[2]

[Anonymous], 1974, Reports on Mathematical Physics, V5, P121, DOI 10.1016/0034-4877(74)90021-4

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