Analysis Seminar

Friday, October 27, 2017 3:30 pm - 3:30 pm EDT (GMT -04:00)

Henna Koivusalo, University of Vienna

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

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 to the theory of self-affine sets.

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 the translations of the affine maps in the iterated function system. 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.

The talk is partly based on joint work with Balazs Barany and Antti Kaenmaki.

MC 5417