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 µ is a Bernoulli measure on E with dimH µ = dimL µ, where dimH and dimL denote Hausdorff and Lyapunov dimensions, then the projection of µ in all but at most one direction has Hausdorff dimension min{dimH µ, 1}. We transfer this result to sets and show that many self-affine sets have projections of dimension min{dimH E, 1} in all but at most one direction.
given by matrices with positive entries. We show that if µ is a Bernoulli measure on E with dimH µ = dimL µ, where dimH and dimL denote Hausdorff and Lyapunov dimensions, then the projection of µ in all but at most one direction has Hausdorff dimension min{dimH µ, 1}. We transfer this result to sets and show that many self-affine sets have projections of dimension min{dimH E, 1} in all but at most one direction.
| Original language | English |
|---|---|
| Pages (from-to) | 473-486 |
| Journal | Annales Academiae Scientiarum Fennicae Mathematica |
| Volume | 42 |
| Issue number | 0 |
| DOIs | |
| Publication status | Published - 31 Dec 2017 |