ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ - ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ

Λεωφ. Κνωσού, 714 09 Ηράκλειο. Τηλ: +30 2810393800, Fax +30 2810393881

Prof. Tamás Keleti

Eötvös Loránd University, Budapest

21 - 9 - 2005

Let be a self-affine set in and let be a "natural" probability measure on . We study the following 3 types of questions:

- Does there exist a (for and ) such that for any
affine map / similarity / isometry / translation

- Is it true that for any
affine map / similarity / isometry / translation ,
iff has non-empty interior in
(that is, contains an elementary part of )?
- Can at least one / most (unless there is some clear obstacle)
can be extended to an
isometry / translation invariant
Borel measure on
such that ?

We have some positive results among others if is a self-similar set with B disjoint parts and also if is self-affine sponge (we get by subdividing a cube into parts uniformly and taking some of them and then iterating this).

joint work with Márton Elekes and András Máthé

Analysis Seminar 2005-09-19