Mathematics – Dynamical Systems
Scientific paper
2009-03-12
Mathematics
Dynamical Systems
20 pages. Some minor errors have been corrected and a few points have been clarified
Scientific paper
We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if $\Lambda$ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of $\Lambda$ in a non-principal direction has Hausdorff dimension $\min(\gamma,1)$, where $\gamma$ is the Hausdorff dimension of $\Lambda$. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
Ferguson Andrew
Jordan Thomas
Shmerkin Pablo
No associations
LandOfFree
The Hausdorff dimension of the projections of self-affine carpets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Hausdorff dimension of the projections of self-affine carpets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hausdorff dimension of the projections of self-affine carpets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-36856