Abstract:

It is known that the Julia set of the McMullen's family z^n+lambda/z^d is a Cantor set of quasicircles if and only if 1/n+1/d<1 (and modulus of lambda is small enough). I will discuss necessity of this kind of arithmetic condition in several examples. In particular, I will introduce Thurston's combinatorial characterization theorem which brings to light obstructions that may occur. Finally, I will focus on a particular family of rational maps obtained by quasiconformal surgery that we are working on with Toni.