Zeros of $\{-1,0,1\}$ Power Series and Connectedness Loci for Self-Affine Sets
Shmerkin, Pablo ; Solomyak, Boris
Experiment. Math., Tome 15 (2006) no. 1, p. 499-511 / Harvested from Project Euclid
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We consider the set $\Om_2$ of double zeros in $(0,1)$ for power series with coefficients in $\{-1,0,1\}$. We prove that $\Om_2$ is disconnected, and estimate $\min \Om_2$ with high accuracy. We also show that $[2^{-1/2}-\eta,1)\subset \Om_2$ for some small, but explicit, $\eta>0$ (this was known only for $\eta=0$). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
Publié le : 2006-05-14
Classification:  Zeros of power series,  self-affine fractals,  30C15,  28A80 
@article{1175789784,
     author = {Shmerkin, Pablo and Solomyak, Boris},
     title = {Zeros of $\{-1,0,1\}$ Power Series and Connectedness Loci for Self-Affine Sets},
     journal = {Experiment. Math.},
     volume = {15},
     number = {1},
     year = {2006},
     pages = { 499-511},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175789784}
}

Shmerkin, Pablo; Solomyak, Boris. Zeros of $\{-1,0,1\}$ Power Series and Connectedness Loci for Self-Affine Sets. Experiment. Math., Tome 15 (2006) no. 1, pp.  499-511. http://gdmltest.u-ga.fr/item/1175789784/