It is possible that example sheets will appear here in the future. The course introduces many of the fundamental ideas in dynamical systems theory and shows how these techniques can be applied to specific physical problems. Convection in a fluid layer heated from below is a classic example of a system in which successive bifurcations lead from a static state through ordered behaviour to disorder. It also has important astrophysical and geophysical applications. The following topics will be covered.
Centre manifolds and normal forms.
Global bifurcations in 2D. 2. Normal forms and normal form symmetries. Location of global bifurcations. The Lorenz equations and chaotic behaviour. Truncations of the PDEs.