Johannes Kellendonk

Abstract

A topological dynamical system is given by a group of homeomorphisms of a topological space X.
The functions from X to X form a semigroup F(X) under composition. The Ellis semigroup E(X) of the dynamical systems is the closure, in the topology of point wise convergence, of its group of homeomorphisms in F(X).
E(X) has a lot of structure, an algebraic structure, a topological structure and a dynamical structure. This is interesting in its own right, but can also be used to characterise the dynamical system. We give an introduction to Ellis semigroups with an emphasis on the algebraic aspects.