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Shadowing, thick sets and the Ramsey property

Published online by Cambridge University Press:  09 January 2015

PIOTR OPROCHA
PIOTR OPROCHA*
Affiliation:
Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059, Kraków, Poland email oprocha@agh.edu.pl
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Abstract

We provide a full characterization of relations between the shadowing property and the thick shadowing property. We prove that they are equivalent properties for non-wandering systems, the thick shadowing property is always a consequence of the shadowing property, and the thick shadowing property on the chain-recurrent set and the thick shadowing property are the same properties. We also provide a full characterization of the cases when for any family ${\mathcal{F}}$ with the Ramsey property an arbitrary sequence of points can be ${\it\varepsilon}$-traced over a set from ${\mathcal{F}}$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1582 - 1595
Copyright
© Cambridge University Press, 2015 

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