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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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  • [1] E. M. Coven, I. Kan, and J. A. Yorke, Pseudo-orbit shadowing in the family of tent maps, Trans. Amer. Math. Soc. 308 (1988), 227-241. MR 946440 (90b:58236)
  • [2] K. Janková and J. Smítal, Characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), 283-292. MR 854575 (87k:58178)
  • [3] T. Pennings and J. Van Eeuwen, Pseudo-orbit shadowing on the unit interval, preprint, 1990. MR 1087487 (92c:54056)
  • [4] A. N. Šarkovskiĭ, On cycles and the structure of a continuous mapping, Ukrain. Mat. Z. 17 (1965), 104-111. (Russian) MR 0186757 (32:4213)
  • [5] J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269-282. MR 849479 (87m:58107)

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Keywords: Iteration, shadowing property, topological dynamics
Article copyright: © Copyright 1992 American Mathematical Society

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