Projective metrics and mixing properties on towers

We study the decay of correlations for towers. Using Birkhoff's projective metrics, we obtain a rate of mixing of the form: c(n)(f, g) less than or equal to Ct alpha (n)parallel tof parallel to paral lel tog parallel to (1) where alpha (n) goes to zero in a way related to the asymptotic mass of upp er floors, parallel tof parallel to is some Lipschitz norm and parallel tog parallel to (1) is some L-1 norm. The fact that the dependence on g is giv en by an L-1 norm is useful to study asymptotic laws of successive entrance times.