Syllabus academic year 2008/2009
(Created 2008-07-17.)

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. FMFN05 overlap following cours/es: FMF090 och FMF092. Optional for: E3, F3, F3tf, N3. Course coordinator: Gunnar Ohlén,, Fysik, kurslaboratoriet. Recommended prerequisits: Elementary mathematics and mechanics. Assessment: Written exam and presentation of a project. Compulsory computor exercise. Parts: 2. Home page:

The course aims at giving an introduction to chaotic systems, i.e. non-linear systems that are deterministic but with a time development which is not predictable over longer periods. The course should give a possibility to reflect over the fascinating phenomena which may show up in chaotic systems, e.g. strange attractors and in this context a basic comprehension of the importance of fractal geometry, or the posibility that the solar system is instable over a longer time scale.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Temporally discrete systems. Feigenbaum’s theory of branching. Dependence on initial values. Fractal geometry with various applications. Different definitons of dimensions

Dissipative systems. Systems of differential equations. Phase space and the Poincaré section. Lyapunov exponents and strange attractors. Coupled oscillators and frequency locking.

Conservative systems and the KAM theory. Hamilton's formalism, integrable systems, billiards, area-preserving maps, chaotic motion in the solar system.

Ohlén, G, Åberg, S, Östborn, P: Chaos, Compendium. Lund 2002


Code: 0109. Name: Chaos.
Higher education credits: 6. Grading scale: TH. Assessment: Written exam. Contents: The theoretical part of the course.

Code: 0209. Name: Project.
Higher education credits: 1,5. Grading scale: UG. Assessment: Presentaion of project. Contents: Project.