Canonical self-affine tilings by iterated function systems

• Autores: Erin P. J. Pearse
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 56, Nº 6, 2007, págs. 3151-3170
• Idioma: inglés
• DOI: 10.1512/iumj.2007.56.3220
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• Resumen

  • An iterated function system Ø consisting of contractive affine mappings has a unique attractor F  Rd which is invariant under the action of the system, as was shown by Hutchinson [3]. This paper shows how the action of the function system naturally produces a tiling T of the convex hull of the attractor. These tiles form a collection of sets whose geometry is typically much simpler than that of F, yet retains key information about both F and Ø. In particular, the tiles encode all the scaling data of Ø. We give the construction, along with some examples and applications. The tiling T is the foundation for the higher-dimensional extension of the theory of complex dimensions which was developed in [13] for the case d . 1.