摘要
用系统演化与参数关系及系统李氏特性指数与参数关系同时对比显示的办法，研究了一类Ｃｒ微分同胚的双曲和非双曲吸引子的动力学．研究发现：①Ｃ２微分同胚测度空间存在双曲与非双曲吸引子集合，而非双曲吸引子又由３个Ｎｅｗｈｏｕｓｅ区间组成，它们可通过对参数ａ的逐段分析法而定出．②双曲型吸引子属结构稳定，而非双曲型吸引子属结构不稳定．③不同类型吸引子的特性用李氏特性指数与参数的关系表示，比通常的表示法更直观。
Dynamics of hyperbolic and nonhyperbolic attractors of [WT5BX〗a Crdiffeomorphisms was studied by simultaneous comparison and display method to show the relationship of systematical evolution versus parameter and systematical lyapunov exponent versus parameter.The study shows:①C2diffeomorphisms measurable space has hyperbolc and nonhyperbolic attractor sets.The nonhyperbolic attractor consists of three Newhouse intervals that can be decided by progressively analytical method for the parameter a.②The hyperbolic attractor is structurally stable.The nonhyperbolic attractor is structurally unstable.③The features of variant attractors expressed by the relation of Lyapunov characteristic exponent versus parameter are much easily seen and sensitive than those of the common expressing method.
出处
《云南大学学报（自然科学版）》
CAS
CSCD
1998年第S1期55-59,共5页
Journal of Yunnan University(Natural Sciences Edition)
基金
云南省教委应用基础研究基金
关键词
李氏指数
结构稳定性
吸引子
Lyapunov exponent,structurally stability,attractor
