Generic behavior of iterated function systems with overlaps

• Autores: Michal Rams
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 218, Nº 1, 2005, págs. 173-186
• Idioma: inglés
• DOI: 10.2140/pjm.2005.218.173
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• Resumen

  • Abstract We prove that for typical self-similar iterated function systems satisfying the transversality condition the number of intersections of cylinders of a given size is for many sizes nearly as small as possible. This implies a result of Solomyak on the absolute continuity of the natural measure and a result of Peres, Simon and Solomyak on the positivity of the packing measure.