Texas A&M
University, Department of
Mathematics, 216 Milner Hall, 4th and 11th of November 2009, 3:00-3:50
Groups and Dynamics Seminar
Simplicial approximations of Julia sets
Volodymyr Nekrashevych of Texas
A&M
University
We will show that the Julia set of any expanding map is an inverse
limit of a sequence of simplicial complexes, which are constructed by a
recurrent combinatorial "cut-and-paste" rule. The construction is a
generalization of such low-dimensional objects as Hubbard trees or
subdivision rules. Our construction can be applied to the study of
Julia set of maps in several variables. Some examples will be
presented.