Resumen de Variational Principle of Topological Pressure of Free Semigroup Actions for Subsets

Qian Xiao, Dongkui Ma

• In this paper, we investigate the relation between topological pressure of free semigroup actions for non-compact sets proposed by Xiao and Ma (J Dynam Differ Equ, 2021) and measure-theoretic pressure of Borel probability measure. For any Borel probability measure, this paper defines lower and upper measure-theoretic pressures.

  Moreover, we give a lower and an upper estimations of the topological pressure of free semigroup actions by local measure-theoretic pressure. In addition, we also show that the topological pressure on a non-empty compact subset K defined in Xiao and Ma (J Dynam Differ Equ, 2021) equals to the supremum of the lower measure-theoretic pressure taken over all probability measures supported on K.