Can one differentiate SRB states with respect to the dynamics? What
about stable-unstable tangencies?
We shall review the differentiability of the map (dynamics)->SRB in the
uniformly hyperbolic case, and discuss the relation with the
susceptibility function. Then we shall show counterexamples to extending
these results to non uniformly hyperbolic dynamics. We discuss then the
case of volume preserving diffeomorphisms, and in particular some positive
results by Dolgopyat. Finally we examine diffeomorphisms with
stable-unstable tangencies, and what might be conjectured for those.