Multifractal analysis of the Brjuno function
成果类型：
Article
署名作者：
Jaffard, Stephane; Martin, Bruno
署名单位：
Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite du Littoral-Cote-d'Opale
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-017-0763-z
发表日期：
2018
页码：
109-132
关键词：
摘要：
The Brjuno function B is a 1-periodic, nowhere locally bounded function, introduced by Yoccoz because it encapsulates a key information concerning analytic small divisor problems in dimension 1. We show that regularity, introduced by Caldern and Zygmund, is the only one which is relevant in order to unfold the pointwise regularity properties of B; we determine its regularity at every point and show that it is directly related to the irrationality exponent : its p-exponent at x is exactly . This new example of multifractal function puts into light a new link between dynamical systems and fractal geometry. Finally we also determine the Holder exponent of a primitive of B.