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MA4H0 Applied Dynamical Systems

Not Running in 2015/16

Lecturer:

Term(s):

Status for Mathematics students: List C for MMath.

Commitment: 30 lectures

Assessment: 3 hour examination 100%.

Prerequisites: There will be no specific prerequisites for the course, although a background in ODES and dynamics, such as MA371 Qualitative Theory of ODEs, would certainly be useful. This material will be reviewed at the beginning and so the main requirement will be a willingness to learn quickly!

Leads To:

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. In particular, motivating examples will be taken from chemical reaction network theory, climate models, fluid motion, celestial mechanics and neuronal dynamics.

The module will be structured around the following topics:

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

Additional Resources

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Year 1 regs and modules
G100 G103 GL11 G1NC

yr2.jpg
Year 2 regs and modules
G100 G103 GL11 G1NC

yr3.jpg
Year 3 regs and modules
G100 G103

yr4.jpg
Year 4 regs and modules
G103

Archived Material
Past Exams
Core module averages