Dynamical systems and ergodic theory
Dynamical systems is the study of any mathematical system where spatial structure evolves with time. Modern approaches may be geometric, topological, probabilistic or computational. I can supervise a range of projects in theoretical dynamical systems and ergodic theory. Many unanswered questions of interest are in random dynamical systems, wherein the particular evolution rules applied are driven by a stochastic process. The theory surrounding classical structures like attractors and invariant measures is quite well worked out in this context, but there is significant scope for developing the theory application of transfer operators for these systems on convenient Hilbert spaces.
Supervisor: Rua Murray
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Analysis, probability, dynamical systems