The Pólya-Chebotarev problem and inverse polynomial images

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2 Citations (Scopus)

Abstract

Consider the problem, usually called the Pólya-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-1n([-1,1]) of a polynomial Tn is always the solution of a certain Pólya-Chebotarev problem. By solving a nonlinear system of equations for the zeros of T2n, we are able to construct polynomials Tn with a connected inverse image.

Original languageEnglish
Pages (from-to)80-94
Number of pages15
JournalActa Mathematica Hungarica
Volume142
Issue number1
DOIs
Publication statusPublished - Feb 2014

Keywords

  • 30C10
  • 41A21
  • analytic Jordan arc
  • inverse polynomial image
  • logarithmic capacity
  • Pólya-Chebotarev problem

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