Equilibrium measures for shift spaces via dimension theory
April 24, 2023 NOON 646 PGH
Abstract
Using a construction analogous to Hausdorff measures, we produce a
measure on a shift space that gives rise to an equilibrium state
provided with certain counting estimates. We give explicit
descriptions of these measures using topological pressure as a
dimensional quantity. We show that this can be done for both one-sided
and two-sided shifts beyond subshifts of finite type. This is joint
work with Vaughn Climenhaga.
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