Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets

DOI10.1080/10586458.2006.10128977zbMath1122.30002arXivmath/0504545OpenAlexW2081837720MaRDI QIDQ5308238

Pablo Shmerkin, B. M. Solomyak

Publication date: 27 September 2007

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504545

zbMATH Keywords

zeros of power seriesself-affine fractals

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Fractals (28A80) Software, source code, etc. for problems pertaining to functions of a complex variable (30-04)

Related Items (18)

Connectedness of attractors of a certain family of IFSs ⋮ Algebraic Number Starscapes ⋮ Overlapping self-affine sets of Kakeya type ⋮ Connectedness locus for pairs of affine maps and zeros of power series ⋮ A characterization of Thurston’s Master Teapot ⋮ Overlapping Iterated Function Systems from the Perspective of Metric Number Theory ⋮ Roots, Schottky semigroups, and a proof of Bandt’s conjecture ⋮ The shape of Thurston's master teapot ⋮ Geometric series with randomly increasing exponents ⋮ On the Fibonacci-Mandelbrot set ⋮ Root sets of polynomials and power series with finite choices of coefficients ⋮ ON THE DIOPHANTINE PROPERTIES OF λ ‐EXPANSIONS ⋮ Multidimensional self-affine sets: non-empty interior and the set of uniqueness ⋮ On self-similar sets with overlaps and inverse theorems for entropy ⋮ Multifractal structure of Bernoulli convolutions ⋮ On Iterated Function Systems with place-dependent probabilities ⋮ Multifractality of overlapping non-uniform self-similar measures ⋮ Typical absolute continuity for classes of dynamically defined measures

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