Ergodic theorem for infinite iterated function systems |
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| Authors: | O Hyong-Chol Ro Yong-hwa Kil Won-gun |
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| 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 |
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| 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. |
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| Keywords: | iterated function system invariant measure ergodic theorem random iterating algorithm |
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