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Ramsey Shadowing and minimal points


Author: W. R. Brian
Journal: Proc. Amer. Math. Soc. 144 (2016), 2697-2703
MSC (2010): Primary 54H20, 37B20, 37B05
DOI: https://doi.org/10.1090/proc/12884
Published electronically: October 5, 2015
MathSciNet review: 3477087
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Abstract: We say that a dynamical system $ X$ has the Ramsey shadowing property if an arbitrary sequence of points in $ X$ can be shadowed on a set that is ``large'' in the sense of Ramsey theory. Our main theorem states that this property is equivalent to the existence of a dense set of minimal points.


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Additional Information

W. R. Brian
Affiliation: Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118
Email: wbrian.math@gmail.com

DOI: https://doi.org/10.1090/proc/12884
Keywords: Ramsey shadowing, minimal points, Ramsey property, ultrafilter limits
Received by editor(s): August 27, 2014
Received by editor(s) in revised form: June 26, 2015
Published electronically: October 5, 2015
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society

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