一类NMIFS吸引子

A Class of Nonlinear Markov Iterated Function System Attractors

中文关键词:  NMIFS吸引子  平衡向量测度  矩.

英文关键词:NMIFS attractor  balanced vector measure  moment.

中文摘要:

      本文给出了NMIFS (Nonlinear Markov Iterated FunctionSystem)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$\hat{M}^{(i)}(i = 1,2, \ldots )$;而对于NMIFS,因$\hat{M}^{(i)}$的计算依赖于$\hat {M}^{(j)}(j \ge i)$,故不能直接计算$\hat{M}^{(i)}$,而只能计算其近似值.

英文摘要:

      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 $\hat {M}^{(i)}~(i = 1,2, \ldots )$ for MIFS, but for NMIFS, we cannot calculate $\hat {M}^{(i)}$ directly because the calculation of $\hat {M}^{(i)}$depends on the value of $\hat {M}^{(j)}(j \ge i)$. So only the approximated value of $\hat {M}^{(i)}$ could be obtained.