Ledrappier-Young formula and exact dimensionality of self-affine measures
Dynamical Systems
2017-08-22 v3
Abstract
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.
Keywords
Cite
@article{arxiv.1511.05792,
title = {Ledrappier-Young formula and exact dimensionality of self-affine measures},
author = {Balázs Bárány and Antti Käenmäki},
journal= {arXiv preprint arXiv:1511.05792},
year = {2017}
}