Equality of pressures for diffeomorphisms preserving hyperbolic measures

For a diffeomorphism which preserves a hyperbolic measure the potential is studied. Various types of pressure of are introduced. It is shown that these pressures satisfy a corresponding variational principle. This research was supported by the grant EU FP6 ToK SPADE2. The author is grateful to IM PAN Warsaw for the hospitality and to C. Wolf for discussions about suitable concepts of pressure.