Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Scrambled sets in shift spaces on a countable alphabet
HTML articles powered by AMS MathViewer

by Brian E. Raines and Tyler Underwood PDF
Proc. Amer. Math. Soc. 144 (2016), 217-224 Request permission

Abstract:

In this paper we characterize the shift spaces which have Li-Yorke chaos (an uncountable scrambled set). We focus primarily on shifts over a countably infinite alphabet. We represent them as either edge-shifts on an infinite graph (the subshift of finite type case) or as labelled edge-shifts on an infinite graph (the sofic shift case). We show in the setting of a subshift of finite type on a shift over a countable alphabet that the shift space has Li-Yorke chaos if, and only if, it has a single scrambled pair, and in this case the scrambled set is closed and perfect (but not necessarily compact). We give an example of a sofic shift over an infinite alphabet which has a single scrambled pair but does not have Li-Yorke chaos.
References
Similar Articles
Additional Information
  • Brian E. Raines
  • Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798–7328
  • MR Author ID: 697939
  • Email: brian_raines@baylor.edu
  • Tyler Underwood
  • Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798–7328
  • Address at time of publication: Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
  • Email: tyler_underwood@umail.ucsb.edu
  • Received by editor(s): July 7, 2014
  • Received by editor(s) in revised form: December 2, 2014
  • Published electronically: June 24, 2015
  • Communicated by: Yingfei Yi
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 217-224
  • MSC (2010): Primary 37B10, 37B20, 37D40, 54H20
  • DOI: https://doi.org/10.1090/proc/12690
  • MathSciNet review: 3415590