A Class of Nonlinear Markov Iterated Function System Attractors

Abstract:

      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.