Content: This course will introduce and develop the notions underlying the geometric theory of dynamical systems and ordinary differential equations. Particular attention will be paid to ideas and techniques that are motivated by applications in a range of the physical, biological and chemical sciences.

The module will be structured around the following topics:

• Review of basic theory: flows, notions of stability, linearization, phase portraits, etc
• Invariant manifold theorems: stable, unstable and center manifolds
• Bifurcation theory from a geometric perspective
• Chaotic dynamics: horsehoes, Melnikov method and discussion of strange attractors

Learning Outcomes: Appreciate the geometric approach to dynamical systems