无穷迭代函数系统的遍历定理

Ergodic Theorem for Infinite Iterated Function Systems

1.
Department of Mathematics and Mechanics, Centre of Basic Sciences, Kim Il Sung University, Pyongyang, D. P. R. of Korea ;

摘要: 度量空间的压缩映射的一个集合称为一个迭代函数系统．凝聚迭代函数系统可以被看成无穷迭代函数系统．研究了紧度量空间上的无穷迭代函数系统．利用Banach极限的特性和均匀压缩性，证明了紧度量空间上无穷迭代函数系统的随机迭代算法满足遍历性．于是，凝聚迭代函数系统的随机迭代算法也满足遍历性．
- 迭代函数系统(IFS) /
- 不变测度 /
- 遍历定理 /
- 随机迭代算法
Abstract: A set of contraction maps of a metric space is called an iterated function systems.Iterated function systems with condensation can be considered infinite iterated function systems.Infinite iterated function systems on compact metric spaces were studied.Using the properties of Banach limit and uniform contractiveness it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces satisfy ergodicity.So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity,too.
- iterated function system /
- invariant measure /
- ergodic theorem /
- random iterating algorithm

[1]	Barnsley M.Fractals Everywhere[M].New York:Academic Press,1988.
[2]	吴亨哲.广义迭代函数系统[J].朝鲜民主主义人民共和国科学院通报，2001,287(5)：3—5.(朝鲜语)
[3]	Elton J.An ergodic theorem for iterated maps[J].Ergodic Theory and Dynamical Systems,1987,7(4)：481—488.
[4]	Forte B，Mendivil F.A classical ergodic property for IFS: A simple proof[J].Ergodic Theory and Dynamical Systems,1998,18(3)：609—611. doi: 10.1017/S0143385798108271
[5]	马东魁，周作领.迭代函数系统的遍历性质——Elton定理的改进[J].应用数学,2001,14(4)：46—50.
[6]	Mendivil F.A generalization of IFS with probability to infinitely many maps[J].Rocky Mountain Journal of Mathematics,1998,28(3)：1043—1051. doi: 10.1216/rmjm/1181071754
[7]	Conway John.A Course of Functional Analysis[M].GTM 96,Springer-Verlag, 1990.