Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure
Dynamical Systems
2020-07-14 v1
Abstract
Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensional real vector space, is exact dimensional. We also establish a Ledrappier-Young type formula for its dimension. The general strategy of the proof is based on the argument given by Feng for the exact dimensionality of self-affine measures.
Keywords
Cite
@article{arxiv.2007.06326,
title = {Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure},
author = {Ariel Rapaport},
journal= {arXiv preprint arXiv:2007.06326},
year = {2020}
}
Comments
43 pages