Abstract:

Singular perturbation of $zn$ give rise to certain one-parameter families of rational maps acting on the Riemann sphere whose Julia sets are homeomorphic to the Sierpinski curve continuum. A common condition among these maps is their escaping critical orbits that eventually enter the immediate basin of infinity after some positive number of iterations.In this talk we address the question of characterizing conjugacy classes ina combinatorial way. To do so, we present a combinatorial model of Sierpinski curve Julia sets for poscritically finite rational maps. In particular, the combinatorialinvariant obtained from the model can be used to characterizes hyperbolic components in the connectedness locus of these rational families.