Dynamically Defined Topological Pressure

Abstract Dynamically defined topological pressure as an extension of the notion of topological pressure for a non compact metric space with a semidynamics is presented. The semi-dynamics of the state space is deduced by a continuous map with a base. Dynamically defined topological pressure from two viewpoints is considered. It is proved that the dynamically defined topological pressure is invariant under special kind of conjugate relations. The properties of pressure for dynamically defined topological pressure are proved.