Multifractal analysis of Birkhoff averages on "self-affine" symbolic spaces
Abstract
We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentiable functions that cannot be deduced from one another by a dilation and a translation. This situation is in contrast with what is observed in the familiar self-similar case. Our results are presented in the framework of almost-multiplicative functions on products of two distinct symbolic spaces and their projection on the associated self-affine carpets.
Keywords
Cite
@article{arxiv.0802.0520,
title = {Multifractal analysis of Birkhoff averages on "self-affine" symbolic spaces},
author = {Julien Barral and Mounir Mensi},
journal= {arXiv preprint arXiv:0802.0520},
year = {2009}
}