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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1165058-X

Keywords:
Shadowing property,
iteration,
zero topological entropy

Article copyright:
© Copyright 1993
American Mathematical Society