FYS4190 – Dynamical Systems and Chaos
Schedule, syllabus and examination date
Course content
- Introduction, Flows, Fixpoints and Stability Analysis
- Bifurcations, Saddle node, Transcritical, Pitchfork and Hopf
- Limit Cycles, Perturbation Analysis of Two-timing
- Maps, Periodic Orbits, Kneading Sequences
- Arnold Tongues, Mode Locking, Synchronization
- Period Doubling, Feigenbaum and Libshaber, Renormalization
- Chaos, Strange Attractors, Poincaré Sections
- 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.
Admission
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.
Prerequisites
Recommended previous knowledge
FYS-MEK1110 – Mechanics, FYS1120 – Electromagnetism, FYS2130 – Oscillations and Waves, FYS2160 – Thermodynamics and Statistical Physics
Teaching
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.
Examination
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.