Résumé
We study the generic invariant probability measures for the geodesic flow on
connected complete nonpositively curved manifolds. Under a mild technical
assumption, we prove that ergodicity is a generic property in the set of
probability measures defined on the unit tangent bundle of the manifold and
supported by trajectories not bounding a flat strip. This is done by showing
that Dirac measures on periodic orbits are dense in that set. In the case of a
compact surface, we get the following sharp result: ergod- icity is a generic
property in the space of all invariant measures defined on the unit tangent
bundle of the surface if and only if there are no flat strips in the universal
cover of the surface. Finally, we show under suitable assumptions that
generically, the invariant probability measures have zero entropy and are not
strongly mixing.