Dynamical Systems (FFR 130)

This course is now taught by Stellan Östlund. The home page below is not up to date. Please refer to the new course home page.


Bernhard Mehlig, 2011/01/26.

Dynamical Systems (FFR 130)

(7.5 credit units)

Examiner:

Bernhard Mehlig
Phone: 772 3452
Office: 7.113

Teachers:

Bernhard Mehlig
Kristian Gustavsson (2 special sessions)
Marina Rafajlovic (examples classes)

New: Hans Fogedby's lecture notes for his lecture on SLE.

New: Examples class on Tuesday. Please see TimeEdit.

New: dates for examples sheets 2010 (see below)

Course evaluation
Students participating in course evaluation

Niklas Schräder
Simon Lindkvist

Schedule

Please refer to TimeEdit.

Abstract

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

Preliminary plan

  1. Introduction
  2. Some definitions and more examples
  3. One-dimensional maps
  4. Chaotic attractors and fractal dimension
  5. Dynamical properties of chaotic systems
  6. Chaos in Hamiltonian systems
  7. Chaotic scattering
  8. Mixing in fluids
  9. Chaos in microlasers
  10. 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 [pdf]
  4. R. Brown, Phil. Mag. 4 (1828) 161 [pdf]
  5. H. A. Kramers, Physica 7 (1040) 284 [pdf]

Lecture notes

Copies of my lecture notes will be made available.

Examples

Homework problems will be set, corrected, and graded . There will be 5 sets of homework problems.

Late submissions are not accepted unless Bernhard has been notified in advance. Please submit your solutions on paper to Marina Rafajlovic.

  1. Sheet 1 (Fri Jan. 29 16:00)
  2. Sheet 2 (Fri Feb. 5 16:00)
  3. Sheet 3 (Wed Feb. 24 16:00)
  4. Sheet 4 (Wed March 3 16:00)
  5. Sheet 5 (Wed March 10 16:00)

Special sessions

Mon Feb 15 10-12 MC Salen (Kristian Gustavsson)
"How to find periodic orbits"

Thu Feb 18 8-10 MC Salen (Kristian Gustavsson)
"How to calculate Lypunov exponents"

Further Resources

Från snökaos till kvantkaos (go to section vetenskap and search for article)

C++ program simulating dynamics of billiard systems.

Stellan Östlund's program illustrating dynamics of standard map (usage).

Reference for turbulence
R. H. Kraichnan, J. Fluid Mech. 67, 155-175 (1975)