Valid for: 2013/14
Decided by: Education Board B
Date of Decision: 2013-04-10
Elective for: F4, F4-tf, N4
Language of instruction: The course will be given in English on demand
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
Competences and skills
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.
Grading scale: TH
Assessment: Written exam and presentation of a project. Compulsory computor exercise.
Parts
Code: 0109. Name: Chaos.
Credits: 6. Grading scale: TH. Assessment: Written exam. Contents: The theoretical part of the course.
Code: 0209. Name: Project.
Credits: 1,5. Grading scale: UG. Assessment: Presentaion of project. Contents: Project
Required prior knowledge: Elementary mathematics and mechanics.
The number of participants is limited to: No
The course overlaps following course/s: FMF090, FMF092
Course coordinator: Universitetslektor Gunnar Ohlén, gunnar.ohlen@matfys.lth.se
Course homepage: http://www.matfys.lth.se/education/FMFN05