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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

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On the absence of invariant measures with locally maximal entropy for a class of $\mathbb {Z}^d$ shifts of finite type
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by E. Arthur Robinson Jr. and Ayşe A. Şahı̇n PDF
Proc. Amer. Math. Soc. 127 (1999), 3309-3318 Request permission

Abstract:

We prove that for a class of $\mathbb Z^d$ shifts of finite type, $d>1$, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.
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Additional Information
  • E. Arthur Robinson Jr.
  • Affiliation: Department of Mathematics, George Washington University, Washington, DC 20052
  • Email: robinson@math.gwu.edu
  • Ayşe A. Şahı̇n
  • Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
  • Email: sahin@plains.nodak.edu
  • Received by editor(s): February 6, 1998
  • Published electronically: May 13, 1999
  • Additional Notes: The research of the first author was partially supported by the NSF under grant number DMS 9303498.
    The research of the second author was partially supported by the NSF under grant number DMS 9501103.
  • Communicated by: Michael Handel
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3309-3318
  • MSC (1991): Primary 28D15; Secondary 28D20
  • DOI: https://doi.org/10.1090/S0002-9939-99-05215-6
  • MathSciNet review: 1646203