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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Shadowing property of continuous maps with zero topological entropy

Author: Milan Kuchta
Journal: Proc. Amer. Math. Soc. 119 (1993), 641-648
MSC: Primary 58F08; Secondary 54H20
MathSciNet review: 1165058
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Abstract: The study of the shadowing property has a long history but for interval maps it is rather new. Recent research in this direction is mainly focused on the positive entropy maps and work for zero entropy is still seldom to be found in the literature. In this paper we give a characterization of zero topological entropy maps which have the shadowing property. Moreover, our condition is necessary for any continuous function to have the shadowing property.

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Keywords: Shadowing property, iteration, zero topological entropy
Article copyright: © Copyright 1993 American Mathematical Society