Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets

Details Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets

2005-04-27

arxiv.org/abs/math/0504545v1

Mathematics

Classical Analysis and ODEs

24 pages, 4 figures

Scientific paper

We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.

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