Projections of self-similar and self-affine fractals
- Prelegent(ci)
- Pablo Shmerkin
- Afiliacja
- University of Manchester
- Termin
- 12 grudnia 2008 10:15
- Pokój
- p. 5840
- Seminarium
- Seminarium Zakładu Układów Dynamicznych
A classical theorem of Marstrand says that for any Borel set E
in the plane of Hausdorff dimension d, the orthogonal projection of E
onto a line with slope t has Hausdorff dimension min(d,1), for almost
every slope t. In general, one can't say anything more than this - the
set of exceptional directions may have full dimension. However, if E has
some additional structure, for example if E is a self-similar set, one
can hope to determine the set of exceptions precisely. I am going to
present some recent progress in this direction, and describe some related
problems which remain open. Parts of my talk will be based on joint work
with A. Ferguson, T. Jordan and Y. Peres.