Absolute continuity of stationary measures.

Resumen: In this talk, we will study random dynamical systems of 
smooth surface diffeomorphisms. Aaron Brown and Federico Rodriguez 
Hertz showed that, in this setting, hyperbolic stationary measures 
have the SRB property, except when certain obstructions occur. Here, 
the SRB property essentially means that the measure is absolutely 
continuous along certain “nice” curves (unstable manifolds). In this 
talk, we want to understand conditions that guarantee that SRB 
stationary measures are absolutely continuous with respect to the 
Lebesgue measure of the ambient space. Our approach is inspired on 
Tsujii’s “transversality” method, which he used to show Palis 
conjecture for partially hyperbolic endomorphisms. This is a joint 
work with Aaron Brown, Homin Lee and Yuping Ruan.