Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Shadowing, entropy and a homeomorphism of the pseudoarc

Author(s): Piotr Koscielniak; Piotr Oprocha
Journal: Proc. Amer. Math. Soc. 138 (2010), 1047-1057.
MSC (2000): Primary 37B45; Secondary 54H20, 37B40, 37B05
Posted: November 10, 2009
MathSciNet review: 2566570
Retrieve article in: PDF

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Abstract: In this article we provide a method of constructing continuous maps $f\colon [0,1]\rightarrow [0,1]$ such that is topologically mixing, has the shadowing property, and the inverse limit of copies of with 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 . We have therefore answered, in the affirmative, a question posed by Chen and Li in 1993.

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