Revista Matemática Iberoamericana

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Volume 35, Issue 3, 2019, pp. 767–804
DOI: 10.4171/rmi/1069

Published online: 2019-04-01

Multifractal phenomena and packing dimension

Frédéric Bayart[1] and Yanick Heurteaux[2]

(1) Université Clermont Auvergne, Aubière, France
(2) Université Clermont Auvergne, Aubière, France

We undertake a general study of multifractal phenomena for functions or measures. We show that the existence of several kinds of multifractal functions or measures can be easily deduced from an abstract statement, leading to new results. This general approach does not work for Fourier or Dirichlet series. Using careful constructions, we extend our results to these cases.

Keywords: Multifractal phenomena, genericity, Hausdorff and packing dimension, Hölder exponent, Fourier series, Dirichlet series

Bayart Frédéric, Heurteaux Yanick: Multifractal phenomena and packing dimension. Rev. Mat. Iberoam. 35 (2019), 767-804. doi: 10.4171/rmi/1069