A Generalization of IFS with Probabilities to Infinitely Many Maps
A Generalization of IFS with Probabilities to Infinitely Many Maps
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DOI：
10.1216/rmjm/1181071754
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发表时间：
1998-09
影响因子：
0.8
通讯作者：
F. Mendivil
中科院分区：
文献类型：
--
作者：
F. Mendivil
本文考虑了将具有概率的IFS的概念从无穷多个映射的情况推广到无穷多个映射的情况。证明了在平均压缩条件下，IFS在Monge-Kantorovich度量下是压缩的.我们还表明，不变分布是连续的参数的IFS。此外，使用Lewellen的结果，我们得到的结果有关的支持不变的措施的吸引子的“几何”IFS。最后讨论了积分关于不变测度的收敛性问题，并给出了这类积分的误差估计。
This paper considers the problem of extending the notion of an IFS with probabilities from the case of nitely many maps in the IFS to the case of innnitely many maps. We prove that under an average contractiv-ity condition the IFS is contractive in the Monge-Kantorovich metric. We also show that the invariant distribution is continuous with respect to the parameters of the IFS. Furthermore, using results of Lewellen , we obtain a result relating the support of the invariant measure to the attractor of the "geometric" IFS. Finally, we discuss the issue of the convergence of integrals with respect to the invariant measure and estimates on the error of these integrals.