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Chain transitivity and variations of the shadowing property

Published online by Cambridge University Press:  03 July 2014

WILLIAM R. BRIAN,
JONATHAN MEDDAUGH and
BRIAN E. RAINES
WILLIAM R. BRIAN
Affiliation:
Department of Mathematics, Tulane University, 6823 St. Charles Ave, New Orleans, LA 70118, USA email wbrian.math@gmail.com
JONATHAN MEDDAUGH
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA email jonathan˙meddaugh@baylor.edu, brian˙raines@baylor.edu
BRIAN E. RAINES
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA email jonathan˙meddaugh@baylor.edu, brian˙raines@baylor.edu
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Abstract

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We show that, under the assumption of chain transitivity, the shadowing property is equivalent to the thick shadowing property. We also show that, if ${\mathcal{F}}$ is a family with the Ramsey property, then an arbitrary sequence of points in a chain transitive space can be ${\it\varepsilon}$-shadowed (for any ${\it\varepsilon}$) on a set in ${\mathcal{F}}$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015, pp. 2044 - 2052
Copyright
© Cambridge University Press, 2014 

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