Hereditarily indecomposable inverse limits of graphs: shadowing, mixing and exactness
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- by Piotr Kościelniak, Piotr Oprocha and Murat Tuncali PDF
- Proc. Amer. Math. Soc. 142 (2014), 681-694 Request permission
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.References
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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
- Email: piotr.koscielniak@im.uj.edu.pl
- 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
- MR Author ID: 765606
- ORCID: 0000-0002-0261-7229
- Email: oprocha@agh.edu.pl
- Murat Tuncali
- Affiliation: Faculty of Arts and Science, Nipissing University, 100 College Drive, Box 5002, North Bay, Ontario, Canada P1B 8L7
- Email: muratt@nipissingu.ca
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 681-694
- MSC (2010): Primary 54F15; Secondary 37E25, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11768-5
- MathSciNet review: 3134008