Multifractal analysis of the Brjuno function

Published 30 Dec 2015 in math.NT and math.DS | (1512.08932v2)

Abstract: We determine the $1$-exponent (according to the Calder\'on-Zygmund definition) of the Brjuno function $B$ everywhere, thus showing that it is a new example of multifractal function. We also discuss various notions of pointwise regularity of the function $B$.

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