Dimension maximizing measures for self-affine systems
Dynamical Systems
2016-04-27 v4
Abstract
In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (K\"aenm\"aki measures). To prove this phenomena, we show that the Ledrappier-Young formula holds for Gibbs measures and we introduce a transversality type condition for the strong-stable directions on the projective space.
Cite
@article{arxiv.1507.02829,
title = {Dimension maximizing measures for self-affine systems},
author = {Balázs Bárány and Michał Rams},
journal= {arXiv preprint arXiv:1507.02829},
year = {2016}
}
Comments
The previous version of the paper has been withdrawn by the author due to a crucial error. It was in the previous version in Section 4, Lemma 4.6 equation (4.4). This error annihilated Theorem 1.2