Multifractal analysis via Lagrange duality
Dynamical Systems
2024-03-01 v2
Abstract
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode the parametric geometry of the Lagrange dual associated with the constrained variational principle. We also give a direct derivation of the Hausdorff dimension of the level sets of the upper and lower local dimensions by exploiting certain weak uniformity properties of the space of Bernoulli measures.
Cite
@article{arxiv.2312.08974,
title = {Multifractal analysis via Lagrange duality},
author = {Alex Rutar},
journal= {arXiv preprint arXiv:2312.08974},
year = {2024}
}
Comments
31 pages, 3 figures. Expository article. v2: slightly more general definition of uniform densities; removal of SSC assumption in Proposition 3.13; numbering changes and improvement of exposition