Entry requirements

120 credits including 90 credits of Mathematics. Real Analysis recommended.

Learning outcomes

On completion of the course, the student should be able to

• calculate periodic orbits and limit cycles and the stability of these;
• calculate bifurcation diagrams for families of dynamic systems;
• account for hyperbolicity, invariant manifolds, homoclinic phenomena and structural stability;
• analyse dynamic systems via symbolic dynamics;
• describe the design of some common strange attractors.

Content

Existence - and uniqueness proofs for solutions to ordinary differential equations, numerical methods, flows, parameter - and initial value dependency, fixed points, periodic orbits, limit cycles, linearisation, stability and Liapunov functions, phase portraits, Poincaré-Bendixson's theorem, Grönwall's lemma, Poincaré maps. Structural stability, symbolic dynamics, conjugation, bifurcation theory, stable and unstable manifolds, homoclinic phenomena, hyperbolicity, chaos and sensitive dependence on initial values, strange attractors. Applications.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.