Universität Wien

250016 VO Selected topics in dynamics (2020S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes

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)


Information

Aims, contents and method of the course

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.

Assessment and permitted materials

Oral examination.

Minimum requirements and assessment criteria

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

Examination topics

Lectures.

Reading list

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.

Association in the course directory

MSTV

Last modified: Mo 03.05.2021 14:48