Entry requirements

120 credits including 90 credits in mathematics. Participation in Real Analysis. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

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

• calculate invariant manifolds and investigate their stability,
• calculate bifurcation diagrams for families of dynamical systems,
• account for hyperbolicity, invariant manifolds, homo- and heteroclinic phenomena and structural stability,
• analyse dynamical systems via symbolic dynamics,
• describe the structure of some common strange attractors.

Content

Flows and maps, invariant manifolds, linearisation, stability, phase portraits, Poincaré maps, structural stability, symbolic dynamics, horseshoes and invariant hyperbolic sets, Sharkovsky's theorem, conjugation, bifurcation theory, stable and unstable manifolds, homo- and heteroclinic phenomena, hyperbolicity, chaos and sensitive dependence on initial values, strange attractors.

Instruction

Lectures and problem solving sessions.

Assessment

Written assignments (6 credits) combined with an oral presentation (4 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.