NMAB23015U Introduction to Dynamical Systems

Volume 2024/2025
Content
  • General Introduction to discrete dynamical systems.
  • Maps in one real dimension
  • Maps in one complex dimension
  • Maps in two real dimensions
  • The shift map and chaotic dynamical systems
  • Symbolic dynamics and subshifts of finite type.
Learning Outcome

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

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

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

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

Competencies:  
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 discrete dynamical systems.
  • Produce proofs of simple results at the level of the course.
  • Use the introduced abstract concepts on concrete problems.
  • Discuss topics from discrete dynamical systems.
  • Explain how discrete 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
Written
Oral
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation)
Exam registration requirements

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

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

Same as 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.