## Dynamical Systems (FFR130)

(7.5 credit units)

See CANVAS at Chalmers for current information.

### Schedule

See TimeEdit at Chalmers for schedule.

## Plan

This course provides and introduction to the subject of chaos in dynamical systems.

Introduction

Some definitions and more examples

One-dimensional maps

Chaotic attractors and fractal dimension

Dynamical properties of chaotic systems

Chaos in Hamiltonian systems

Chaotic scattering

Mixing in fluids

Chaos in microlasers

Advection of small particles in turbulent flows

## Literature

1. Chaos in dynamical systems, E. Ott, Cambridge University Press, Cambridge 1993 (reprinted with corrections 1993, 1997).

2. Classical and quantum chaos: a cyclist treatise, P. Cvitanovic et al. See in particular chapter 17 Fixed points and how to get them.

3. A. Einstein, Ann. Phys. 17 (1905) 549

4. R. Brown, Phil. Mag. 4 (1828) 161

5. H. A. Kramers, Physica 7 (1040) 284 [pdf]

## Examination

Credits for this course are obtained by solving the homework set (solutions of examples and programming projects). There will be five sets of homework which are graded.

Every student must hand in her/his own solution on paper. Same rules as for written exams apply: it is not allowed to copy any material from anywhere unless appropriate reference is given. All figures must have axis labels and captions giving all information necessary to reproduce the figure. Describe your results in words. Always compare with theory. Summarise problems, discuss possible reasons. Program code must be appended. Each of the five examples sheet gives 5 points. In order to pass the course at least 14 points are required. The examples sheets will be processed by URKUND. Your solutions should be submitted before the deadline as PDF files electronically to

### Homework problems

Sheet 1 [pdf]

Sheet 2 [pdf]

Sheet 3 [pdf]

Sheet 4 [pdf]

Sheet 4 [pdf]