摘要
In this article the theory of NMIFS （Nonlinear Markov Iterated Function System） and the construction method of an NMIFS are presented. The balanced vector measure and the recursive calculation of the ＂moment＂ of a class of NMIFS attractors are discussed, and the structure characteristics are analyzed. The result shows that we can calculate the moments ^M^（i） （i = 1, 2,...） for MIFS, but for NMIFS, we cannot calculate ^M^（i） directly because the calculation of ^M^（i）depends on the value of ^M^（j） （j ≥ i）. So only the approximated value of ^M^（i）could be obtained.
本文给出了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”的递归计算,分析了NMIFS吸引子的结构特征．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)的计算依赖于M(j)(j≥i),故不能直接计算M(i),而只能计算其近似值．
基金
the National Natural Science Foundation of China (60573172)
the Superior University Science Technology Research Project of Liaoning province (20040081).
