Entropy and measures at the boundary
François Ledrappier (CNRS-Paris)

We describe equivariant families of measures on the boundary of the universal cover of a closed Riemannian manifold with negative curvature. We discuss the associated entropy and its rigidity pro- perties. The same formalism can describe:

1.the Patterson-Sullivan family and the associated Burger-Roblin measure,
2.the Lebesgue family and the Liouville measure,
3.the harmonic measures and the drifted harmonic measures,
4.the Mohsen family giving the Rayleigh quotient and
5.the Gibbs-Patterson families.