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Dal'nevost. Mat. Zh., 2017, Volume 17, Number 2, Pages 201–209 (Mi dvmg354)  

This article is cited in 1 scientific paper (total in 1 paper)

On the lemniscates of rational functions

V. N. Dubinina, A. S. Afanaseva-Grigorevab

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: The impact of the connectivity of some lemniscates of the rational function on the absolute value of its derivative is considered. The role of the lemniscates in the problems of the extremal decomposition of the Riemann sphere is discussed.

Key words: rational function, lemniscate, extremal decomposition, condenser capacity, symmetrization

Funding Agency Grant Number
Russian Science Foundation 14-11-00022


Full text: PDF file (519 kB)
References: PDF file   HTML file
UDC: 517.54
MSC: Primary 30C10; Secondary 30C15
Received: 12.06.2017

Citation: V. N. Dubinin, A. S. Afanaseva-Grigoreva, “On the lemniscates of rational functions”, Dal'nevost. Mat. Zh., 17:2 (2017), 201–209

Citation in format AMSBIB
\Bibitem{DubAfa17}
\by V.~N.~Dubinin, A.~S.~Afanaseva-Grigoreva
\paper On the lemniscates of rational functions
\jour Dal'nevost. Mat. Zh.
\yr 2017
\vol 17
\issue 2
\pages 201--209
\mathnet{http://mi.mathnet.ru/dvmg354}
\elib{http://elibrary.ru/item.asp?id=32239883}


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    This publication is cited in the following articles:
    1. V. N. Dubinin, “Poyas lemniskat i teoremy iskazheniya dlya mnogolistnykh funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 33, Posvyaschaetsya pamyati Galiny Vasilevny KUZMINOI, Zap. nauchn. sem. POMI, 458, POMI, SPb., 2017, 17–30  mathnet
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