On controlled specification and uniqueness of the equilibrium state in expansive systems

摘要

In Bowen (1974/75 Math. Syst. Theory 8 193-202), Bowen showed that for an expansive system (X, T) with specification and a potential empty set with the Bowen property, the equilibrium state is unique and fully supported. We generalize that result by showing that the same conclusion holds for weakened versions of Bowen's hypotheses in which constant parameters are replaced by any increasing unbounded functions f(n) and g(n) with sublogarithmic growth (in n).