2 7 A pr 2 00 5 ZEROS OF { − 1 , 0 , 1 } POWER SERIES AND CONNECTEDNESS LOCI FOR SELF - AFFINE SETS
نویسنده
چکیده
We consider the set Ω2 of double zeros in (0, 1) for power series with coefficients in {−1, 0, 1}. We prove that Ω2 is disconnected, and estimate minΩ2 with high accuracy. We also show that [2 − η, 1) ⊂ Ω2 for some small, but explicit η > 0 (this was only known for η = 0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
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