Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 252–258 | Cite as

Uniformization of Simply-Connected Ramified Coverings of the Sphere by Rational Functions

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Abstract

We deduce a systemofODEs describing behavior of critical points and poles of a smooth one-parametric family of rational functions uniformizing a given family of ramified coverings of the Riemann sphere.

Keywords and phrases

Riemann surface ramified covering rational function uniformization conformal mapping one-parametric family 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.N. I. Lobachevskii Institute of Mathematics and MechanicsKazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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