Date(s) - 21/02/2020
11 h 00 min - 12 h 00 min
FRUMAM, St Charles (2ème étage)
Dierk SCHLEICHER (I2M, Aix-Marseille Université)
We discuss two concepts of how to measure how “complicated” Julia sets of polynomials are. The first, investigated among others by Stas Smirnov, measures how many points of the Julia set are “endpoints”. The other, introduced by William Thurston under the name of “core entropy”, concerns the entropy of the dynamics restricted to interesting invariant subsets of the Julia set. These two concepts are closely related.
We present research projects (in cooperation with two of our undergraduate students) that investigate and improve upon both of these topics. The central idea is to interpret these questions in terms of symbolic dynamics and in particular in the combinatorics of words.