MAT9820 – Complex Dynamics
Schedule, syllabus and examination date
The course is an introduction to the classical topic of one variable complex dynamics. We study iterations of a map from the Riemann sphere to itself, which we divide into a chaotic part (the Julia set) and an orderly part (the Fatou set). In the first part of the course we use mostly basic complex analysis, and in the second part we use potential theory. This allows us to describe statistical properties of the dynamical system.
After completing the course you will have knowledge of the basic theory about the following, and be able to use the knowledge to solve problems:
- complex dynamics on the Riemann sphere;
- local dynamics: fixed points and periodic points;
- global dynamics: Fatou- and Julia sets, self similarity, classification of periodic Fatou components, Sullivan’s non-wandering theorem;
- topological entropy and invariant measures;
- equilibrium measure: potentials and quasi-potentials, construction of the equilibrium measure, equidistribution, mixing, Lyapounov exponents.
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
10 credits overlap with MAT4820 – Complex Dynamics
* For information about the potential partial overlap with other courses, contact the Department.
4 hours of lectures/exercises per week throughout the semester.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Final oral examination, including oral presentation of a topic of own choice and following examination.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.