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Proceedings of the American Mathematical Society

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

 

 

Shadowing property of continuous maps


Authors: Tomáš Gedeon and Milan Kuchta
Journal: Proc. Amer. Math. Soc. 115 (1992), 271-281
MSC: Primary 58F12; Secondary 58F20
MathSciNet review: 1086325
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Abstract: We study continuous maps of an interval into itself. We find the necessary and sufficient condition for the maps of the type $ {2^n}$ to have the shadowing property. Further we show that any chaotic map, which has only cycles of order a power of 2, does not have the shadowing property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1086325-3
Keywords: Iteration, shadowing property, topological dynamics
Article copyright: © Copyright 1992 American Mathematical Society