The Dynamics of Semigroups of Contraction Similarities on the Plane

Given a parametrized family of Iterated Function System (IFS) we give sufficient conditions for a parameter on the boundary of the connectedness locus, M, to be accessible from the complement of M.

Moreover, we provide a few examples of such parameters and describe how they are connected to Misiurewicz parameter in the Mandelbrot set, i.e. the connectedness locus of the quadratic family z^2+c.