Local dimensions of self-similar measures satisfying the finite neighbour condition

Kathryn Hare, Alex Rutar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
3 Downloads (Pure)

Abstract

We study sets of local dimensions for self-similar measures in R satisfying the finite neighbour condition, which is formally stronger than the weak separation condition (WSC) but satisfied in all known examples. Under a mild technical assumption, we establish that the set of attainable local dimensions is a finite union of (possibly singleton) compact intervals. The number of intervals is bounded above by the number of non-trivial maximal strongly connected components of a finite directed graph construction depending only on the governing iterated function system. We also explain how our results allow computations of the sets of local dimensions in many explicit cases. This contextualises and generalises a vast amount of prior work on sets of local dimensions for self-similar measures satisfying the WSC.
Original languageEnglish
Pages (from-to)4876-4904
Number of pages29
JournalNonlinearity
Volume35
Issue number9
DOIs
Publication statusPublished - 11 Aug 2022

Keywords

  • Iterated function system
  • Self-similar
  • Local dimension
  • Multifractal analysis
  • Weak separatopm condition

Fingerprint

Dive into the research topics of 'Local dimensions of self-similar measures satisfying the finite neighbour condition'. Together they form a unique fingerprint.

Cite this