混沌分形图特征计算机评价的轨道再现测试

Visualization and Test of the Dynamics-Characteristic Orbits Embedded in Chaos and Fractal Images with Computers

通过计算机再现混沌分形图轨道的测试方法,分析评价了不同混沌分形图的结构特征.研究表明,轨道再现测试是探索混沌分形图特征的一种有效方法,它可以形象地显示混沌分形图的动力学特征.直观地跟踪M集分形图点的轨道,通过测试和统计,可以实现周期性等特征的计算机证明;牛顿变换J集动力平面上轨道的再现测试,不仅直观地描述了牛顿变换f映射的某些动力学特征,而且,证明了f映射在J集附近具有初始条件敏感依赖的混沌特性.测试具有D4对称特性的平面排列动力系统的周期轨道,可以发现广义M集周期区域对充满Julia集中周期轨道的影响规律.

The structure characteristics of different chaos and fractal images can be evaluated by reproducing the dynamics orbits in these images.It is a useful method to discover the dynamics characters of chaos and fractal images.Directly tracking orbits relative to a parameter on an area of M set,the computer proof of some characteristics,such as periodicity,can be realized by this kind of test.Reproducing and testing the orbits in the filled-in Julia sets from Newton mappings not only shows some dynamics characters of the mappings,but also shows the chaos characteristic which means the sensitivity to the initial conditions near Julia sets.Testing the plane-tiling dynamics systems with D_4 symmetry,the affecting rules between period areas of general M sets and period orbits in filled-in Julia sets can be understood.