Texas A&M University, Department of
Mathematics, 216 Milner Hall, 6th of February 2008, 3:00-3:50
Groups and Dynamics Seminar
On the Julia set of
a rational endomorphism of CP^2
Volodymyr Nekrashevych of Texas A&M
University
I will present a combinatorial model of the Julia set of the
post-critically finite rational function $[z, p]\to [(1-2z/p)^2,
(1-2/p)^2]$. The function was studied 16 years ago by J.E.Fornaess and
N.Sibony, but only very general facts were known since then. Our model
describes the Julia set as a direct limit of three-dimensional
polyhedra, which are constructed by a relatively simple inductive
procedure. Some interesting objects, like an uncountable family of
triangle-filling dendrites will be discussed.