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Transactions of the American Mathematical Society

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A topological classification of locally constant potentials via zero-temperature measures


Authors: Christian Wolf and Yun Yang
Journal: Trans. Amer. Math. Soc. 372 (2019), 3113-3140
MSC (2010): Primary 37B10, 37D35, 37L40
DOI: https://doi.org/10.1090/tran/7659
Published electronically: May 20, 2019
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Abstract: We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures and the boundary of higher dimensional generalized rotation sets. We also discuss the regularity of the localized entropy function on the boundary of the generalized rotation sets.


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Additional Information

Christian Wolf
Affiliation: Department of Mathematics, The City College of New York, New York, New York 10031; The Graduate Center, CUNY, New York, New York 10016
Email: cwolf@ccny.cuny.edu

Yun Yang
Affiliation: Department of Mathematics, The Graduate Center, CUNY, New York, New York 10016
Email: yyang@gc.cuny.edu

DOI: https://doi.org/10.1090/tran/7659
Received by editor(s): August 30, 2017
Received by editor(s) in revised form: June 1, 2018, and June 27, 2018
Published electronically: May 20, 2019
Article copyright: © Copyright 2019 American Mathematical Society