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The dimension of projections of self-affine sets and measures (1511.03556v1)
Published 11 Nov 2015 in math.DS and math.CA
Abstract: Let E be a plane self-affine 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 self-affine sets have projections of dimension min{dim_H E,1} in all but at most one direction.