Johannes Kellendonk : "Ellis semigroup of bijective substitutions"
→
Europe/Paris
M7 411 (UMPA)
M7 411
UMPA
Description
The Ellis semigroup (or envelopping semigroup) of a topological dynamical system (X,T) is the compactification of T in the topology of pointwise convergence on the set of functions X -> X.
Its topological and algebraic structure characterise the dynamical system.
It is not so easy to calculate explicit examples which go beyond the case in which the Ellis semigroup is actually a group. I will show that this is, however, possible for the dynamical systems associated to bijective substitutions with trivial generalised height. The Thue-Morse substitution is the simplest example.
These dynamical systems are not tame. As an application I show that they are semi-regular in the sense of Auslander-Glasner.