The Quasi-Periodic Centre-Saddle Bifurcation
The Quasi-Periodic Centre-Saddle Bifurcation
复制标题
DOI：
10.1006/jdeq.1997.3365
复制
发表时间：
1998-01
影响因子：
2.4
通讯作者：
H. Hanßmann
中科院分区：
文献类型：
--
作者：
H. Hanßmann
摘要在正规抛物不变环的邻域内，考虑了哈密顿系统的近可积族。在可积的情况下，这样的环面分成正常椭圆和正常双曲不变环面。用Kam理论方法证明了正常抛物环面和分叉情形都经受住了由相关大Cantor集参数表示的不可积摄动。这些结果被应用于刚体动力学。
Abstract Nearly integrable families of Hamiltonian systems are considered in the neighbourhood of normally parabolic invariant tori. In the integrable case such tori bifurcate into normally elliptic and normally hyperbolic invariant tori. With a KAM-theoretic approach it is shown that both the normally parabolic tori and the bifurcation scenario survive a non-integrable perturbation, parametrised by pertinent large Cantor sets. These results are applied to rigid body dynamics.