Variational principle for packing topological pressure of nonautonomous dynamical systems

TL;DR

This paper establishes a variational principle linking packing topological pressure and measure-theoretic pressure in nonautonomous dynamical systems, expanding the theoretical understanding of pressure concepts in such systems.

Contribution

It introduces a variational principle for packing topological pressure in nonautonomous systems, connecting it with measure-theoretic pressures and providing new theoretical insights.

Findings

Proved a pressure distribution principle for Pesin topological pressure.

Established a Billingsley type theorem for packing topological pressure.

Derived an upper bound for packing topological pressure on generic points.

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.