Connectedness locus for pairs of affine maps and zeros of power series

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We study the connectedness locus N for the family of iterated function systems of pairs of affine-linear maps in the plane (the non-self-similar case). First results on the set N were obtained in joint work with P. Shmerkin [11]. Here we establish rigorous bounds for the set N based on the study of power series of special form. We also derive some bounds for the region of " -transversality" which have applications to the computation of Hausdorff measure of the self-affine attractor. We prove that a large portion of the set N is connected and locally connected, and conjecture that the entire connectedness locus is connected. We also prove that the set N has many zero angle "cusp corners," at certain points with algebraic coordinates. [ABSTRACT FROM AUTHOR]
Original languageAmerican English
Pages (from-to)281-308
Number of pages28
JournalJournal of Fractal Geometry
Issue number3
StatePublished - 2015


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