{-1，0，1}-幂级数的零点与自仿射集的连通轨迹
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
摘要：
考虑系数在{-1，0，1}中的幂级数在（0，1）中的双零点集W.我们证明了W是不连通的，并高精度地估计了W的最小值。我们还证明了[2^（-1/2）-e，1）包含在W中，对于一些小的，但明确的e>0（这是只知道为e=0）。这些结果在自仿射分形的无穷Bernoulli卷积和连通性的研究中有应用。
英文摘要：
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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