Variational principle for topological tail pressures with sub-additive upper semi-continuous potentials

Abstract

ABSTRACTThe topological tail pressure and the conditional pressure are defined for sub-additive upper semi-continuous potentials via separated subsets and refining sequences of partitions in topological dynamical systems with finite topological entropy respectively. By proving the equivalence of the topological tail pressure and the conditional pressure with respect to the refining sequence of essential partitions, we present a variational principle for the topological tail pressure without any additional assumptions. The properties of the topological tail pressure including the power rule, the product rule and the natural extension are also discussed.