The dimension of projections of selfaffine sets and measures
Abstract
Let E be a plane selfaffine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu is a Bernoulli measure on E with dim_H mu = dim_L mu, where dim_H and dim_L denote Hausdorff and Lyapunov dimensions, then the projection of mu in all but at most one direction has Hausdorff dimension min{dim_H mu,1}. We transfer this result to sets and show that many selfaffine sets have projections of dimension min{dim_H E,1} in all but at most one direction.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.03556
 Bibcode:
 2015arXiv151103556F
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Classical Analysis and ODEs