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

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.

Improvements have been made for the previous version, 19 pages