Dimensions of sets arising from iterated function systems -- with a special emphasis on self-affine sets

Henna Koivusalo (University of Vienna)

Tuesday 15th August, 2017 16:00-17:00 Maths Seminar Room (level 3)

Abstract

In this colloquium style talk I will review the history of calculating 
dimensions of sets that arise as invariant sets of iterated function 
systems. I will, in particular, compare the theory of self-similar sets 
(where the set is a union of shrunk copies of itself) to the theory of 
self-affine sets (where the set is a union of affine images of itself).

One of the most important results in the dimension theory of self-affine 
sets is a result of Falconer from 1988. He showed that Lebesgue almost 
surely, the dimension of a self-affine set does not depend on 
translations of the pieces of the set. A similar statement was proven by 
Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine 
measures. At the end of my talk I will explain an orthogonal approach to 
the dimension calculation, introducing a class of self-affine systems in 
which, given translations, a dimension result holds for Lebesgue almost 
all choices of deformations.

This work is joint with Balazs Barany and Antti Kaenmaki.

Add to your calendar

Download event information as iCalendar file (only this event)