Proceedings of the American Mathematical Society

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

Author(s): E. Arthur Robinson Jr.; Ayse A. Sahin
Journal: Proc. Amer. Math. Soc. 127 (1999), 3309-3318.
MSC (1991): Primary 28D15; Secondary 28D20
Posted: May 13, 1999
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Abstract: We prove that for a class of $\mathbb Z^d$ shifts of finite type,

, 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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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: 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
Posted: 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 of article: Copyright 1999, American Mathematical Society

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