Alex Rutar

Multifractal analysis


Multifractal analysis is, generally speaking, the study of the regularity properties of a locally rough function. Such objects typically exhibit very rich local behaviour: for many of the well-studied examples, the level sets of the functions are dense in their support and are often very large (in the sense of Hausdorff dimension) for a continuum of values.

Much of my work has focused on the geometry of overlapping self-similar iterated function systems for the “hard” range of q<0: see for example my WSC paper or my multifractal decomposition paper. I have also worked on the multifractal analysis of random substitutions.

Relevant Publications

  1. Multifractal analysis of measures arising from random substitutions
    With: Andrew Mitchell
    Journal: Preprint (submitted)
    Links: pdfarxiv
  2. A multifractal decomposition for self-similar measures with exact overlaps
    Journal: Preprint (submitted)
    Links: pdfarxiv
  3. Local dimensions of self-similar measures satisfying the Finite Neighbour Condition
    With: Kathryn E. Hare
    Journal: Nonlinearity 35 (2022), 4876–4904
    Links: pdfdoizblarxiv
  4. Geometric and combinatorial properties of self-similar multifractal measures
    Journal: Ergodic Theory Dyn. Syst. 43 (2023), 2028–2072
    Links: pdfdoizblarxiv