ON A NEW CLASS OF ANOSOV ACTIONS

For every irreducible Riemannian symmetric space S of non-compact type we study a finite family of Anosov actions (in the sense of Hirsch, Pugh and Shub) of reductive Lie groups. If the rank of S is equal to 1, then these actions coincide with the geodesic flow. As in this special case the resulting orbit spaces carry an invariant symplectic structure.