An example of a pathological random perturbation of the Cat Map
Tanya Yarmola

I am going to discuss an example of a "statistical attractor" for the Cat
Map subject to certain random perturbations. The perturbed system has a
unique singular invariant measure supported on a small interval of the
stable manifold around the fixed point. This singular measure depends only
on the size of the perturbation and yet the push-forward images of any other
measure on the torus converge to it.