On the packing dimension of box-like self-affine sets in the plane

Jonathan M. Fraser*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We consider a class of planar self-affine sets which we call 'box-like'. A boxlike self-affine set is the attractor of an iterated function system (IFS) consisting of contracting affine maps which take the unit square, [0, 1](2), to a rectangle with sides parallel to the axes. This class contains the Bedford-McMullen carpets and the generalizations thereof considered by Lalley-Gatzouras, Baranski and Feng-Wang as well as many other sets. In particular, we allow the mappings in the IFS to have non-trivial rotational and reflectional components. Assuming a rectangular open set condition, we compute the packing and box-counting dimensions by means of a pressure type formula based on the singular values of the maps.

Original languageEnglish
Pages (from-to)2075-2092
Number of pages18
JournalNonlinearity
Volume25
Issue number7
DOIs
Publication statusPublished - 15 Jun 2012

Keywords

  • Iterated function systems
  • Finite-type condition
  • Hausdorff dimension
  • Fractals
  • Constructions

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