Variational principle for packing topological pressure of nonautonomous dynamical systems

Abstract: We investigate the relationship between various topological pressures and the corresponding measure-theoretic pressures for nonautonomous dynamical systems based on the Carath\'eodory-Pesin structure. We prove a pressure distribution principle for Pesin topological pressure and a Billingsley type theorem for packing topological pressure. We then obtain a variational principle for packing topological pressure, which reveals a variational relation between the packing pressure and measure-theoretic upper local pressure. We further examine the applicability of our findings to a typical nonautonomous dynamical system, wherein the sequence of continuous selfmaps preserves the same Borel probability measures. In addition, we derive an upper bound for the packing topological pressure on the set of generic points.