NMAB23015U Introduction to Dynamical Systems

Volume 2023/2024
  • General Introduction to dynamical systems.
  • Maps in one dimension
  • Maps in two dimensions
  • Differential equations in two dimensions
  • ODE’s in higher dimensions
  • Maps in the complex plane
  • Subshifts of finite type.
Learning Outcome

By the end of the course the student is expected to have:

  • In depth knowledge of fundamental results and methods in dynamical systems.
  • Knowledge of the concrete dynamical systems presented in during the course.
  • Understanding of the many and diverse appearances and applications of dynamical systems.

By the end of the course the student is expected to be able to 

  • Analyze and qualified argue for results on dynamical systems.
  • Produce proofs for theorems in line with those appearing in the course.
  • Solve exercises posed during the course.


By the end of the course the student is expected to be able to 

  • Follow and reproduce arguments and applications of abstract notions and concepts from dynamical systems.
  • Produce proofs of simple results at the level of the course.
  • Use the introduced abstract concepts on concrete problems.
  • Discuss topics from dynamical systems.
  • Explain how dynamical systems and results about dynamical systems enter in various applications.

See Absalon for a list of course literature.

Topology or similar and Kompleks funktionsteori (KomAn) or similar.
5 hours of lectures and 3 hours of problem-solving per week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 130
  • Theory exercises
  • 21
  • Exam Preparation
  • 19
  • Exam
  • 1
  • Total
  • 206
7,5 ECTS
Type of assessment
Oral examination, 30 minutes, no preparation time
Exam registration requirements

The student must have received approval of 4 out of 5 possible hand-ins.

All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as the ordinary exam.

In the event that the student has not obtained approval of 4 out of 5 possible hand-ins before the ordinary exam. The student must, in order to do the reexam, have handed in the missing hand-ins at least 3 weeks prior to the re-exam and have received approvals at least 2 weeks before the reexam.

Criteria for exam assesment

The student must demonstrate satisfactorily that they meet the subject’s objective description.