Continuity of Green functions of Hausdorff continuous regular compact sets on the parameter space

In the work of Lyubich, Mane-Sad-Sullivan it was studied of stability and bifurcation theory of a family of rational maps depending on a parameter space $M$. In particular they proved that Hausdorff continuity of Julia sets implies stability and vice-versa. In this work we study relation between Haussdorf continuous regular compact sets and continuity of their Green functions on the parameter space.