Topological entropy for set valued maps |
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Authors: | Marek Lampart Peter Raith |
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Institution: | a Mathematical Institute of the Silesian University in Opava, Silesian University of Opava, Na Rybní?ku 1, 746 01 Opava, Czech Republic b Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria |
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Abstract: | Any continuous map T on a compact metric space X induces in a natural way a continuous map on the space K(X) of all non-empty compact subsets of X. Let T be a homeomorphism on the interval or on the circle. It is proved that the topological entropy of the induced set valued map is zero or infinity. Moreover, the topological entropy of is zero, where C(X) denotes the space of all non-empty compact and connected subsets of X. For general continuous maps on compact metric spaces these results are not valid. |
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Keywords: | 37B40 37B99 37E05 37E10 37B10 |
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