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Attractors of Iterated Function Systems with uncountably many maps

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 نشر من قبل Giorgio Mantica
 تاريخ النشر 2015
  مجال البحث فيزياء
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We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are uncountably many and the set of their fixed points is a Cantor set. We prove that when this latter either is the attractor of a finite, non-singular, hyperbolic, I.F.S. (of first generation), or it possesses a particular dissection property, the attractor of the second generation I.F.S. consists of finitely many closed intervals.



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