A discrete dynamical systems consists of a space of states X (population size, say) and a continuous function f from X to itself that describes how these states evolve with time. Typically X is a compact metric space and topological dynamics is the study of the structural and asymptotic aspects of this behaviour.
This project could investigate one of a number of aspects of topological dynamics that I am interested in. For example:
1. definitions of chaos;
2. characterizations of invariant subsets such as omega limit sets;
3. course graining of complex systems to simpler systems;
4. hyperbolicity and shadowing;
5. induced maps, for example on inverse limit spaces or hyperspaces.
I am also interested in what might be called generalized topological dynamics and abstract topological dynamics. Generalized topological dynamics, the generalization of topological dynamics to topological spaces in general, rather compact metric spaces. Abstract topological dynamics asks the following question: given a function f on a set X, when is there a useful topology on X with respect to which f is continuous.
You can get a better idea of the sorts of questions I am interested in by looking at my papers: http://web.mat.bham.ac.uk/C.Good/
This project may be eligible for a college or EPSRC scholarship in competition with all other PhD applications.
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FTE Category A staff submitted: 40.00
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