Ergodic Theorem for Infinite Iterated Function Systems

O Hyong-chol; Ro Yong-hwa; Kil Won-gun

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O Hyong-chol, Ro Yong-hwa, Kil Won-gun. Ergodic Theorem for Infinite Iterated Function Systems[J]. Applied Mathematics and Mechanics, 2005, 26(4): 426-430.

Citation:

O Hyong-chol, Ro Yong-hwa, Kil Won-gun. Ergodic Theorem for Infinite Iterated Function Systems[J]. Applied Mathematics and Mechanics, 2005, 26(4): 426-430.

Citation:

O Hyong-chol, Ro Yong-hwa, Kil Won-gun. Ergodic Theorem for Infinite Iterated Function Systems[J]. Applied Mathematics and Mechanics, 2005, 26(4): 426-430.

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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 ;

Received Date: 2003-11-03
Rev Recd Date: 2004-11-16
Publish Date: 2005-04-15

Abstract

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

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References(7)

References

[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.