2017
May
16

# Dynamics seminar: Karoly Simon (Budepest): Singularity of self-similar measures (Joint with Lajos Vago)

2:00pm to 3:00pm

We consider self-similar Iterated Function System (IFS) on the
line constructed with overlapping cylinders. Recently there have been a
number of outstanding results which have suggested that the overlap has
dramatic change in the most important properties of the IFS only if there is
an exact overlap between some of the cylinders.
In this talk, we point out that this is not always the case, at least as far
as the absolute continuity of self-similar measures is concerned.
Namely, we present some one-parameter families of homogeneous self-
similar measures on the line such that