Slicing the Sierpiński gasket

Balázs Bárány, Andrew Ferguson, Károly Simon

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We investigate the dimension of intersections of the Sierpiński gasket with lines. Our first main result describes a countable, dense set of angles that are exceptional for Marstrand's theorem. We then provide a multifractal analysis for the set of points in the projection for which the associated slice has a prescribed dimension.

Original languageEnglish
Pages (from-to)1753-1770
Number of pages18
JournalNonlinearity
Volume25
Issue number6
DOIs
Publication statusPublished - Jun 1 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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