This course is discontinued

FYS4190 – Dynamical Systems and Chaos

Schedule, syllabus and examination date

Choose semester

Course content

  1. Introduction, Flows, Fixpoints and Stability Analysis
  2. Bifurcations, Saddle node, Transcritical, Pitchfork and Hopf
  3. Limit Cycles, Perturbation Analysis of Two-timing
  4. Maps, Periodic Orbits, Kneading Sequences
  5. Arnold Tongues, Mode Locking, Synchronization
  6. Period Doubling, Feigenbaum and Libshaber, Renormalization
  7. Chaos, Strange Attractors, Poincaré Sections
  8. Scaling, Fractals, Multifractals, Self Organized Criticality

Learning outcome

The course offers an introduction to the modern theory of dynamical systems. The students will learn to analyze non-linear systems described by maps and differential equations and get familiar with the concepts of chaos and fractals.


Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


There will be 6 hours education a week, 3 hours lectures and three hours tutorial lectures. Towards the end of the course, each student will pick a subject for a written project that will be defended at a final oral exam.


Oral presentation of project work. Letter grade.

Examination support material

No examination support material is allowed.

Language of examination

You may submit your response in Norwegian, Swedish, Danish or English. If you would prefer to have the exam text in English, you may apply to the course administrators.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course






Every spring

The course is offered if at least 4 students are registered.


Every spring

Teaching language

Norwegian (English on request)

This course will not be taught in spring 2010