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WANG Hui, FAN Qinjie
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Abstract: Let (X,d)be a compact metric space, f: X→X a continuous map, and (K(X),H) a compact metric space consisting of all nonempty compact subsets of X. It has been proved that the topological ergodicity of setvalued map is equivalent to the topological double ergodicityof f by studying the relation between the motion of points and the motion of sets; moreover, a compactsystem has been constructed which has zero topological entropy and no chaotic property, but the inducedset valued map of which has infinite to pological entropy and distributional chaos, this implies that the topological complexity of could be far greater than that of f.
Key words: setvalued map, topological ergodicity, topological entropy, distributional chaos
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WANG Hui, FAN Qinjie. Topological Ergodicity, Entropy and Chaos of Setvalued Discrete Systems[J].J4, 2007, 45(06): 903-906.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2007/V45/I06/903
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