Colloquium Mathematics, Prof.dr. M. Dekking (UD)

03 December 2013

Join us for coffee and tea at 15.30 p.m.

Date: Tuesday, December 3^rd 2013
Speaker: Michel Dekking (University Delft)
Room: 5161.0293 (Bernoulliborg)
Time: 16.15

Title: The isomorphism problem for substitution dynamical systems.

Abstract:

Substitutions are maps from the letters of an alphabet to the set of words over the alphabet. Suppose such a map is expanding, in the sense that the iterates of the substitution give longer and longer words. Then in many cases the substitution will determine at least one bi-infinite word over the alphabet. The closed orbit under the shift of this infinite word is called a substitution dynamical system. Two dynamical systems are isomorphic if there exists a bi-continuous bijection between them which preserves the dynamics. The task is to decide when two substitutions generate isomorphic dynamical systems. A substitution is called uniform if all the images of the letters have the same length. A first result is that the number of uniform substitutions with the same length that generate isomorphic systems is finite, if the substitutions are one-to-one and if we ignore changes of the alphabet. We will present the isomorphism class of the Toeplitz morphism 0 -> 01>, 1 -> 00. This is joint work with Ethan Coven and