Introductory description

This course will introduce and develop the notions underlying the geometric theory of dynamical systems and ordinary differential equations.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will be structured around the following topics:

• Review of basic theory: flows, notions of stability, linearization, phase portraits, etc;
• `Solvable' systems: integrability and gradient structure, applications in celestial mechanics and chemical reaction networks;
• Invariant manifold theorems: stable, unstable and center manifolds;
• Bifurcation theory from a geometric perspective;
• Compactification techniques: flow at infinity, blow-up, collision manifolds;
• Chaotic dynamics: horsehoes, Melnikov method and discussion of strange attractors;
• Singular perturbation theory: averaging and normally hyperbolic manifolds.

Learning outcomes

By the end of the module, students should be able to:

• See outline syllabus.

Subject specific skills

See outline syllabus

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.