Course manual 2025/2026

Course content

Dynamics in one complex variable, focussed on the iterative behavior of polynomials and rational functions.

 

We will treat local behavior near fixed points, introduce Fatou and Julia sets and prove their basic properties. The course will follow course notes by Lukas Geyer, which are freely available via https://www.math.montana.edu/geyer/2016-fall-m597/materials/s2016-complex-dynamics-notes.pdf. These notes are partially based on the excellent but less elementairy book by Milnor, titled Dynamics in one Complex Variable, third edition. Exercises from Milnor's book will be assigned every two weeks.

 

Requirements for this course are bachelor level courses in complex analysis and topology. Some background in dynamical systems will be useful, but is required.

 

If possible given the number of students, each student will give a one-hour presentation on one of the topics during the second half of the course.

 

The final grade is determined by three components: the final exam (65%), bi-weekly homework exercises (20%), a one-hour lecture during the course (15%). The homework exercises can only count in your favor, if not the grade is given by 65/80 times the final exam grade, and 15/80 times the lecture grade.

 

In order to pass the course, the final exam grade should be at least 5.0 (not rounded). If lower, the final exam grade determines the total grade. 

Study materials

Literature

Objectives

  • You will know and should be able to reproduce the main definitions, presented in sections 1-12 in the book by Milnor.
  • You will know the most important results from sections 1-12 in the book by Milnor.
  • You will be able to apply the main techniques used in the proofs in sections 1-12 in the book by Milnor.

Teaching methods

  • Lecture

Learning activities

Activity

Hours

Hoorcollege

28

Tentamen

3

Self study

137

Total

168

(6 EC x 28 uur)

Attendance

This programme does not have requirements concerning attendance (TER-B).

Assessment

Item and weight Details

Final grade

1 (100%)

Tentamen

The final grade is determined by three components: the final exam (65%), bi-weekly homework exercises (20%), a one-hour lecture during the course (15%).

Assignments

Every two weeks homework exercises will be handed in, counting for 20%.

 

Students are encouraged to study together on the exercises. However, every student should hand in their own written or typed solutions, and include in their solutions the names of other students with whom they solved the exercises.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

WeeknummerOnderwerpenStudiestof
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

Contact information

Coordinator

  • prof. dr. H. Peters

Lecturers

Han Peters

Misha Hlushchanka