English

Intermediate dimensions -- a survey

Metric Geometry 2021-02-08 v3 Dynamical Systems

Abstract

This article surveys the θ\theta-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ=0\theta=0 to box-counting dimensions when θ=1\theta=1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.

Keywords

Cite

@article{arxiv.2011.04363,
  title  = {Intermediate dimensions -- a survey},
  author = {Kenneth J. Falconer},
  journal= {arXiv preprint arXiv:2011.04363},
  year   = {2021}
}

Comments

18 pages, 2 figures. Further examples and open problems have been added

R2 v1 2026-06-23T20:00:38.034Z