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), 3309-3318

MSC (1991):
Primary 28D15; Secondary 28D20

DOI:
https://doi.org/10.1090/S0002-9939-99-05215-6

Published electronically:
May 13, 1999

MathSciNet review:
1646203

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-05215-6

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