Equality of pressures for diffeomorphisms preserving hyperbolic measures

TL;DR

This paper investigates the pressure associated with diffeomorphisms preserving hyperbolic measures, establishing a variational principle for various types of pressure related to the unstable Jacobian.

Contribution

It introduces and analyzes different types of pressure for the potential related to the unstable Jacobian, proving they satisfy a variational principle.

Findings

Pressures satisfy a variational principle

Various types of pressure are introduced and studied

The potential relates to the Jacobian on unstable manifolds

Abstract

For a diffeomorphism which preserves a hyperbolic measure the potential $\phi^u=-\log|{\rm Jac} df|_{E^u}|$ is studied. Various types of pressure of $\phi^u$ are introduced. It is shown that these pressures satisfy a corresponding variational principle.