Universität Wien

250109 VO Selected topics in Dynamical Systems (2018S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 01.03. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.03. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.03. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.03. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.03. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.03. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.04. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.04. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.04. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.04. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.04. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.04. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.04. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.05. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.05. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.05. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.05. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.05. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.05. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.06. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.06. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.06. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.06. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.06. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.06. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.06. 12:00 - 13:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.06. 13:00 - 13:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Fractal geometry is a relatively young field of mathematics, studying sets that have a lot of fine detail at all levels of magnification. Its current methodology combines dynamical systems and geometric measure theory.

In this lecture course we will cover basics of fractal geometry. We will discuss the following topics:
- 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
- basics of geometric measure theory: projection, slicing, product theorems, rectifiability, Kakeya problem etc
If necessary, prerequisites from measure theory will be recalled as appropriate for methodology and proofs.

Assessment and permitted materials

Oral examination through presentations if appropriate.

Minimum requirements and assessment criteria

Understanding the constructions and definitions and how to use them.

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 07.09.2020 15:40