Reproducing Kernel Hilbert Space methods in dynamical systems

Host Faculty: Engineering
General Subject Area: Pure Mathematics
Project Level: PhD
View the Research Website
FIND A PROJECT - Engineering

Nonlinear dynamical systems can admit a plethora of invariant and transient objects, including invariant manifolds and invariant measures that are distinguished as important in some way or other. These objects are often glocal rather than local, have no explicit formula, but are characterised via functional relations that are hard to solve. The underlying dynamical systems induce transfer operators on spaces of observables, providing a linear, but infinite dimensional framework in which to work. Transfer operators are difficult to access numerically, and this project examines the approximation of such operators in Reproducing Kernel Hilbert Spaces (RKHSs). Specific types of problems include: computation of eigenfunctions of Koopman and Perron-Frobenius operators, stability of finite rank approximation on RKHSs, Bayes inspired learning of an unknown system.  (PhD only, Pure or Applied Mathematics)


Supervisor: Rua Murray

Does the project come with funding


Final date for receiving applications



 Dynamical systems and analysis