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arXiv · 1306.6170

The Polya-Chebotarev problem and inverse polynomial images

Klaus Schiefermayr
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Abstract

Consider the problem, usually called the P\'olya-Chebotarev problem, of finding a continuum in the complex plane including some given points such that the logarithmic capacity of this continuum is minimal. We prove that each connected inverse image $\T_n^{-1}([-1,1])$ of a polynomial $\T_n$ is always the solution of a certain P\'olya-Chebotarev problem. By solving a nonlinear system of equations for the zeros of $\T_n^2-1$, we are able to construct polynomials $\T_n$ with a connected inverse image.

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Klaus Schiefermayr. 2013-06-26. The Polya-Chebotarev problem and inverse polynomial images. https://arxiv.org/abs/1306.6170

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