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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the absence of invariant measures
with locally maximal entropy
for a class of ${\mathbb Z}^d$ shifts of finite type


Authors: E. Arthur Robinson Jr. and Ayse A. Sahin
Journal: Proc. Amer. Math. Soc. 127 (1999), 3309-3318
MSC (1991): Primary 28D15; Secondary 28D20
Published electronically: May 13, 1999
MathSciNet review: 1646203
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Abstract | References | Similar Articles | Additional Information

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

Ayse A. Sahin
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
Email: sahin@plains.nodak.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05215-6
PII: S 0002-9939(99)05215-6
Keywords: Ergodic theory, $\mathbb Z^d$ actions, entropy, symbolic dynamics
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
Article copyright: © Copyright 1999 American Mathematical Society