Absolute continuity of self-similar measures on the plane

Boris Solomyak, Adam Śpiewak

Consider an iterated function system consisting of similarities on the complex plane of the form $g_i(z)={\lambda }_{i}z+t_i,{\lambda }_i,t_i\in \mathbb{C},|{\lambda }_i|<1,i=1,\dots ,k$. We pro…