On the absence of invariant measures with locally maximal entropy for a class of shifts of finite type
Authors:
E. Arthur Robinson Jr. and Ayse A. Sahin
Journal:
Proc. Amer. Math. Soc. 127 (1999), 33093318
MSC (1991):
Primary 28D15; Secondary 28D20
Published electronically:
May 13, 1999
MathSciNet review:
1646203
Fulltext PDF Free Access
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Abstract: We prove that for a class of 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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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/S0002993999052156
PII:
S 00029939(99)052156
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
