Positive entropy equilibrium states

2017/08/07 by Climenhaga, Vaughn, Cyr, Van
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.02272

Abstract

For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological entropy. We give a non-uniform specification condition under which this property continues to hold, and demonstrate that it does not necessarily hold for other non-uniform versions of specification that have been introduced elsewhere.

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