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
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