Exceptional sets for self-affine fractals

• Autores: Kenneth J. Falconer, Jun Miao
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 3, 2008, págs. 669-684
• Idioma: inglés
• DOI: 10.1017/s0305004108001576
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• Resumen

  • Under certain conditions the "singular value function" formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.