Universität Wien FIND

250016 VO Selected topics in dynamics (2020S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik


Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").


Sprache: Englisch




Tuesday 10:00-11:30 BZ09 (During e-learning: zoom, contact me for details)
Thursday 14:00-14:45 BZ09 (During e-learning: zoom, contact me for details)
(The Thursday lecture is followed by the AG Ergodentheorie Seminar at 15:15, which might also be of interest to participants)


Ziele, Inhalte und Methode der Lehrveranstaltung

Fractal geometry studies the fine structure of sets and measures. Its current methodology combines dynamical systems and geometric measure theory.
In this lecture course we will cover the basics of fractal geometry. We will discuss the following topics:
- quasi self-similarity of sets
- fractal sets through iterated function systems
- the role of symbolic dynamics in studying fractals
- definitions and comparison of different notions of dimension: box, packing, Hausdorff, etc
- dynamical dimension formulas
- measures on fractals
- applications to other fields (Number theory, probability theory, etc.)
If necessary, prerequisites from measure theory will be recalled as appropriate for methodology and proofs.

For Information regarding Home-Learning please see my personal homepage (https://www.mat.univie.ac.at/~troscheit/teaching.html) or contact me by email.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Oral examination.

Mindestanforderungen und Beurteilungsmaßstab

Understanding the constructions and definitions and how to apply course results.




All the necessary material will be covered in class. However:
Falconer: Fractal Geometry - Mathematical Foundations and Applications, John Wiley, Third Edition, 2014
Mattila: Geometry of sets and Measures in Euclidean Spaces, Cambridge University Press, 1999
are good reading, but more suggested reading will be given during the course.

Zuordnung im Vorlesungsverzeichnis


Letzte Änderung: Mo 03.05.2021 14:48