Shadowing, entropy and a homeomorphism of the pseudoarc

Kościelniak, Piotr; Oprocha, Piotr

doi:10.1090/S0002-9939-09-10162-4

Shadowing, entropy and a homeomorphism of the pseudoarc
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by Piotr Kościelniak and Piotr Oprocha PDF

Proc. Amer. Math. Soc. 138 (2010), 1047-1057 Request permission

Abstract:

In this article we provide a method of constructing continuous maps $f\colon [0,1]\rightarrow [0,1]$ such that $f$ is topologically mixing, has the shadowing property, and the inverse limit of copies of $[0,1]$ with $f$ as the bonding map is the pseudoarc. Such a map can be obtained as an arbitrarily small $\mathcal {C}^0$-perturbation of any topologically exact map on $[0,1]$. We have therefore answered, in the affirmative, a question posed by Chen and Li in 1993.

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