Fractal geometry and dynamics
| Where | University of Jyväskylä |
|---|---|
| When | Spring 2026, Period 3 |
| Language | English |
| Updated | October 7, 2025 |
| Contact | alex@rutar.org |
Recent updates
This is the course webpage for the upcoming course fractal geometry and dynamics to be taught in Spring 2026, Period 3 (January 8 to March 15, 2026). As more information becomes available I will add it here.
If you have any questions please email me at the email above.
Course description
The goal of this course is to provide an introduction to fractal geometry from the perspective of dynamical systems theory. A particular emphasis is given on objects with some form of invariance under re-scaling, such as self-similarity.
A key intermediate goal is to introduce dynamical systems theory, which (for us) is a useful frame of reference for understanding invariance. This is a ubiquitous tool in analysis, PDEs, mathematical physics, geometry, engineering, …
Some topics which will be covered:
- Hausdorff dimension of sets and measures
- Measure preserving systems
- Ergodic theorems
- Entropy
- Conditional measures, Rokhlin disintegration
- Exact dimensionality of self-similar measures
Related courses:
Pre-requisites
The following pre-requisites are essential.
- Measure and integration 1 & 2
- Introductory probability theory
Evaluation
The current plan is that course evaluation will be based on exercises and a presentation with a written (5-10 pages) and oral component (45-60 minutes).
Course material
This course will be primarily based on comprehensive lecture notes, which will be linked here when they are finished (approx. December 2025).
These notes are based on the following references:
- Self-similar and self-affine sets and measures by Balázs Bárány, Károly Simon, and Boris Solomyak. Email me if you want a PDF copy.
- Mike Hochman’s ergodic theory notes.
- Marcelo Viana’s notes on Rokhlin disintegration.