Hausdorff dimensions of self-similar and self-affine fractals in the Heisenberg group

• Autores: Zoltán M. Balogh, Jeremy T. Tyson
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 1, 2005, págs. 153-183
• Idioma: inglés
• DOI: 10.1112/s0024611504015205
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• Resumen

  • We study the Hausdorff dimensions of invariant sets for self-similar and self-affine iterated function systems in the Heisenberg group. In our principal result we obtain almost sure formulae for the dimensions of self-affine invariant sets, extending to the Heisenberg setting some results of Falconer and Solomyak in Euclidean space. As an application, we complete the proof of the comparison theorem for Euclidean and Heisenberg Hausdorff dimension initiated by Balogh, Rickly and Serra-Cassano.