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Proceedings of the American Mathematical Society

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Hereditarily indecomposable inverse limits of graphs: shadowing, mixing and exactness

Authors: Piotr Kościelniak, Piotr Oprocha and Murat Tuncali
Journal: Proc. Amer. Math. Soc. 142 (2014), 681-694
MSC (2010): Primary 54F15; Secondary 37E25, 54H20
Published electronically: October 22, 2013
MathSciNet review: 3134008
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Abstract: We provide a method of construction of topologically mixing maps $ f$ on topological graph $ G$ with the shadowing property and such that the inverse limit with $ f$ as the single bonding map is a hereditarily indecomposable continuum. Additionally, $ f$ can be obtained as an arbitrarily small perturbation of any given topologically exact map on $ G$, and if $ G$ is the unit circle, then $ f$ is necessarily topologically exact.

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Additional Information

Piotr Kościelniak
Affiliation: Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Prof. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland

Piotr Oprocha
Affiliation: AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland — and — Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland

Murat Tuncali
Affiliation: Faculty of Arts and Science, Nipissing University, 100 College Drive, Box 5002, North Bay, Ontario, Canada P1B 8L7

Keywords: Continuum, hereditarily indecomposable, inverse limit, mixing, shadowing
Received by editor(s): October 16, 2011
Received by editor(s) in revised form: March 19, 2012
Published electronically: October 22, 2013
Additional Notes: The second author is the corresponding author.
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.