Supervisor: Dr Reem Yassawi
Project description:
In this project the postgraduate researcher will investigate the computation and algebraic structure of two topological invariants of some symbolic dynamical systems.
In these systems, which consist of a topological space and a group acting on the space, both space and time are discretised. The space is a totally disconnected set, consisting of infinite configurations of symbols with various constraints. While the space is often nontrivial to study, the group action is simple and consists of shifting configurations. These systems arise as codings of dynamical systems acting on an interval in the real line.
Topological invariants are objects associated to a dynamical system which help distinguish it from other systems. One topological invariant that gives important information about a dynamical system is the automorphism group, whose elements are generalised symmetries of the system under study. A second topological invariant is the Ellis semigroup, which is a compactification of the group action. There are existing techniques in the recent literature to describe the computation of these two invariants, and the role of the researcher is to study these techniques, and then to extend them to the proposed family of dynamical systems. In some cases the automorphism group can be recovered from the Ellis semigroup, and the researcher will also investigate the existence of such connections between these two invariants. The candidate should have a strong formation in analysis and topology, and a basic understanding of discrete dynamical systems. Knowledge and experience in programming will be an asset to driving intuition.
Further information:
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