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Ergodic theorem for infinite iterated function systems
Authors:O Hyong-Chol  Ro Yong-hwa  Kil Won-gun
Affiliation:Department of Mathematics and Mechanics, Centre of Basic Sciences,; Kim Il Sung University, Pyongyang, D.P.R.of Korea;;Pyongyang Railway University, Pyongyang, D.P.R.of Korea;;Department of Applied Mathematics, Tongji University, Shanghai 200092, P.R.China
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.
Keywords:iterated function system  invariant measure  ergodic theorem  random iterating algorithm
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