矩阵迭代与图象序列

Matrix Iteration and Image Sequences

反映动力系统特征的迭代过程常常给出异常复杂的几何结构.熟知的复二次迭代过程向人们展示了Julia集和Mandebrot集，大量的文献给出了复二次迭代过程的各种推广形式。本文研究了一类矩阵迭代过程及其吸引子；探讨该过程的吸引子的性质；考查线性与非线性过程的差异;着重研究迭代矩阵为一类Hudamard矩阵时迭代吸引子的性质；考虑了高阶离散动力系统的推广形式及存在问题；并在计算机上完成了一些有趣的图象.本文研究表明，这类迭代过程的吸引子依赖于迭代矩阵的谱半径。

Iteration procedures that present the characteristics of dynamic system always produce very complicated geometric construction. Well-known two-degree complex iteration processes exhibit the sets of Julia and Mandebrot. Many general forms have been given about two-degree complex iteration process. In this paper, the iteration matrix and attractors for a kind of complex iterative schemes are investigated. The properties of attractors given from the schemes are discussed. The differences between linear and nonlinear schemes are checked. When the iterative matrix is of Hadamard type, the properties of attractors are discussed. The generalization and some of its problems for higher degree discrete dynamic systems are pointed out in the paper. Also some interes ting images on computer are shown and the conclusion is that attractors of the iterative schemes are dependent On the nlatrix 's spectral radius.