Multifractal analysis of the Brjuno function
Number Theory
2017-11-15 v2 Dynamical Systems
Abstract
We determine the -exponent (according to the Calder\'on-Zygmund definition) of the Brjuno function everywhere, thus showing that it is a new example of multifractal function. We also discuss various notions of pointwise regularity of the function .
Keywords
Cite
@article{arxiv.1512.08932,
title = {Multifractal analysis of the Brjuno function},
author = {Stéphane Jaffard and Bruno Martin},
journal= {arXiv preprint arXiv:1512.08932},
year = {2017}
}
Comments
to appear in Invent. Math., this arXiv version contains a few more details than the one to be published