Regularity of invariant densities for 1D-systems with random switching
  This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points. 
Yuri Bakhtin, Tobias Hurth and Jonathan C. Mattingly
math.DS math.PR