Syllabus academic year 2007/2008

Higher education credits: 6. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in English on demand. FMF090 overlap following cours/es: FMFN05. Optional for: D3, E3, F3, F3tf, N3, Pi4, V4. Course coordinator: Professor Ingemar Ragnarsson,, Fysik, kurslaboratoriet. Recommended prerequisits: Calculus in severable variables, basic linear algebra and mechanics. Assessment: The grading is based on the result of the written exam. 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