根据关联维数的计算方法，对健康人、冠心病人及健康犬的心电渡形进行了计算与分析。得出如下结论；（1）心脏系统的运动落在具有非整数维的奇异吸引子上，即心脏系统的运动是混沌的；（2）健康心脏系统的运动比病理状态复杂；（3）随着物种的进化，混沌性可能愈加显著。

推广了Baker, Devaney和Romera等的工作，并构造出一系列得指映射的广义Mandel-brot-Julia集（简称广义M-J集）。采用实验数学的方法，做如下工作：给出了复数阶广J集发生突变的理论依据；众理论上分析了广义M-J集的对称性和周期性；给出了复数阶广义M集周期花瓣分布的新的相邻规则；发现了复数阶广义M集包含了广义J集构造的大量信息；复数阶广义M-J集的分形生长速度要快于实数阶广义M-J集的分形生长速度，参数λo的值决定了广义J集的分形生长速度，复数阶广义M集的分形生长指向多分岔点和Misiurewicz点。

给出了NMIFS（nonlinear markov iterated function system）理论与构造NMIFS吸引子的方法，讨论了一类NMIFS吸引子的平衡向量测度和“矩”分析了NMIFS吸引子的结构物特征. 研究结果表明：对于MIFS，可以通过递归方法来计算矩M（i)（I=1，2，…）；而对于NMIFS，因M（i)（j≥i），故不能直接计算M（i)，而只能计算其近似值。

In orderlo stody the iatefior strcture of the Mandelbrot (M) set. Pickover and Hooper have ad-wwed the epsilon cross method and the star trails method. respectively. In order to reveal the exterior structure of the Mset. Philip has proposed the regional decomposition method and the angle-slicing decompoaition method. In this pa-per. these methods-are extended. and the equipolenfial line method and the color adjustment method are proposod to study the exterior struture of the M set. A series of the non-boundary region structure images of the generalized M sets is generated by using the above-mentioned methode. The results show that the non-boundary regions of the generalized M sets for intexer index number have the fraetal feature; while those for decimal index number have diseontlnuity and col-lapse, and their erolutions depend on the choice of the principal range of the phase angle.

In order to show details of fractal structure of Mandelbrot set precisely, Lyapunov exponents and periodic scanning techniques have been brought forward by Shirri and Welstead. This paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized Mandelbrot–Julia sets (the generalized M-J sets). Adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized M-J sets generated from the complex mapping z→zα+c(α∈R), and explores structure and distributing of periodicity "petal" and topological law of periodicity orbits of the generalized Msets, and finds that the generalized Mset contains abundant information of structure of the generalized J sets by founding the whole portray of the generalized J sets based on the generalized Mset qualitatively. Furthermore, the physical meaning of the generalized M-J sets have been expounded.