双曲极限圆映射的混沌吸引子及充满Julia集

目的构造双曲平面上极限圆中的混沌吸引子和广义充满Julia集．方法从双曲几何的角度分析了极限圆的内部结构及对称特性，将双曲映射限制在基本域内，并利用双曲极限圆基本域中点之间的距离特性，直接采用欧氏平面李雅普诺夫指数计算方法判断选定参数向量下动力系统的动力学特性．结果在基本域中可以采用这一方法判断选定参数向量下的双曲极限圆动力系统的动力学特性．结论根据对极限圆内部结构的剖析和对该双曲映射在参数空间各选定参数向量下的动力学特性的判断，可以大量生成极限圆的混沌吸引子及广义充满Julia集．

Chaotic Attractors and Generalized Filled-in Julia Sets from Mapping with Hyperbolic Limit Disc

The authors aim to construct the chaotic attractors and generalized filled-in Julia sets in the limit disc in the hyperbolic plane.According to the symmetry characteristic of hyperbolic limit disc,the mapping is restricted in the fundamental region.Because the distance between points in this region can be calculated via the Euclidean distance function,the method of testing Lyapunov exponent in the Euclidean plane is directly used to judge the characteristic of the dynamics of the chosen parameter vectors.As a result,using the method mentioned above,a great lot of chaotic attractors and generalized filled-in Julia sets of limit disc can be generated.