New Variational Principles of Topological Pressures

We introduce three types of topological pressures and measure-theoretic pressures, present three variational principles between these measure-theoretic pressures and the corresponding topological pressures, and show that the upper capacity topological pressure of the whole space is determined by the Pesin–Pitskel topological pressure of dynamical balls under some suitable assumptions. Moreover, we show that these measure-theoretic pressures are equivalent for nonsingular measures.