【摘要】 ChungK.W.等人利用双曲对称群的生成元构造出了具有[p,q]+对称的双曲极限圆迭代映射.为了进一步研究这个迭代映射,本文构造出它的参数空间的广义M集.提出一个实用、简便的搜索参数组合的方法,解决了在选择构造广义M集的参数断面时的盲目性问题.按照排列组合方法,将所有参数两两组合,在计算机屏幕上按序构造出所有参数断面的粗略的广义M集块.从这样的组合图上挑选出对[p,q]+双曲极限圆动力系统影响较大的参数组合,并进一步在这样的参数组合下构造出广义M集.从这种广义M集的不同参数区域挑选参数,成功地构造出了混沌吸引子、充满Julia集形式的双曲极限圆图案,成功地构造出了用同一组参数构造既有混沌吸引子又有充满Julia集的混合形式的双曲极限圆图案.更多还原

【Abstract】 Dr.Chung K.W.etc constructed a mapping of hyperbolic limit disc with the hyperbolic symmetry group [p,q]+.To further investigate the mapping,we construct its general M sets in parameter space.We present an effective and convenient method to search the parameter combination,which wipes out the blind possibility of selecting parameters as an intersection plane.According to permutation and combination,we can curtailly and orderly construct all drafts of M sets about each combination of parameters in computer screen.Several combinations of parameters,selected from above mentioned drafts,have importantly influence to the dynamic systems when they are changed.These combinations can be used to construct general M set.We succsessfully generate hyperbolic limit discs with the forms of chaotic attractors and filled-in Julia sets by selecting parameters from the M sets.Moreover,we successfully generate the hyperbolic limit disc with the mixture of chaotic attractor and filled-in Julia set with the same group of parameters in the same pattern.更多还原