Course syllabus

# Kaos

Chaos

## FMFN05, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Chaos

Valid for: 2018/19

Decided by: PLED F/Pi

Date of Decision: 2018-03-28

Elective for: BME4, 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

- have a general knowledge about system conditions leading to chaotic and regular behaviour, respectively.
- be familiar with mathematical methods used to analyse chaotic systems
- have a general understanding why it is useful to introduce dimensions which are not integer

Competences and skills

For a passing grade the student must

- be able to apply mathematical methods used for the description of non-linear systems
- be able to analyse the time development of a system and be able to determine if the system is chaotic or regular
- be able to determine which mathematical models are appropriate in different situations
- be able to determine the dimension of simple fractals

*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 - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam and presentation of a project. Compulsory computor exercise.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

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

- Ohlén, G, Åberg, S, Östborn, P: Chaos, Compendium. Lund 2006.

Course coordinator: Sven Åberg, sven.aberg@matfys.lth.se

Course homepage: http://www.matfys.lth.se/education/FMFN05