Equality of pressures for diffeomorphisms preserving hyperbolic measures

Abstract

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

Accepted for publication in Mathematische Nachrichten