Course manual 2025/2026

Course content

In this course we will discuss the differences between deterministic and random dynamical systems, and the new phenomena arising when the dynamics is subject to random noise. We plan to discuss the following topics

Chaos Game and Iterated Function Systems
Products of random matrices, Lyapunov exponents
Random dynamical systems as skew product systems, ergodic theory of skew products
Stochastic stability

Objectives

Learn basic notions in ergodic theory for random dynamical systems, including hyperbolicity and Lyapunov exponents.
Learn theory of skew products, for instance understand the difference between quenched and annealed results.
Learn theory of stochastic stability.

Teaching methods

Lecture
Presentation/symposium
Self-study

Learning activities

Activity	Hours
Hoorcollege	26
Self study	142
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

Grades are determined by homework assignments and a final presentation

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

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

Contact information

Coordinator

prof. dr. Ale Jan Homburg

prof. dr. Evgeny Verbitskiy

Owner	Master Mathematics
Coordinator	prof. dr. Ale Jan Homburg
Part of	Master Mathematics, specialization Algebra and Geometry, year 1 Master Mathematics, specialization Analysis and Dynamical Systems, year 1 Master Mathematics, specialization Stochastics , year 1 Master Mathematics, specialisation Discrete Mathematics and Quantum Information, year 1

Random Dynamical Systems