Unstable Topological Pressure for Partially Hyperbolic Diffeomorphisms with Sub-additive Potentials

TL;DR

This paper introduces a new concept of unstable topological pressure for partially hyperbolic diffeomorphisms with sub-additive potentials and establishes a variational principle linking it to entropy and Lyapunov exponents.

Contribution

It defines unstable topological pressure in this context and proves a variational principle without additional assumptions.

Findings

Established the variational principle for unstable topological pressure

Connected unstable pressure with measure theoretic entropy and Lyapunov exponents

Extended the theory to C^1-smooth partially hyperbolic diffeomorphisms

Abstract

In this paper, we introduce the unstable topological pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. Moreover, without any additional assumption, we have established the expected variational principle which connects this unstable topological pressure and the unstable measure theoretic entropy, as well as the corresponding Lyapunov exponent.