Stationary measures on projective spaces.

Let V be a real finite dimensional vector space,
G a semisimple subgroup of the linear group GL(V),
and m a probability measure on G whose support spans
a Zariski dense subgroup of G.
We will see that the set of
ergodic stationary probability measures
on the projective space P(V) is in bijection
with the set of compact G-orbits in P(V).
This is a joint work with JF. Quint.