14 citations · 66 across the 17 of their papers we have counts for
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Blaschke product for bordered surface
Andrei Bogatyrev
It is well known that a ramified holomorphic covering of a closed unitary disc by another such a disc is given by a finite Blaschke product. The inverse is also true. In this note…
Water flow under rectangular dam
Andrei Bogatyrëv, Oleg Grigor'ev
A new analytical method for calculation the characteristics of the flow in porous medium bounded by a rectangular polygonal path is proposed. The method is based on the usage of hi…
Capacity of several aligned segments
Andrei B. Bogatyrev, Oleg A. Grigoriev
In this note we present a universal formula in terms of theta functions for the Log- capacity of several segments on a line. The case of two segments was studied by N.I.Akhiezer (1…
How many Zolotarev fractions are there?
Andrei Bogatyrev
Known properties of Chebyshev polynomials are the following: they have simple critical points with only two (finite) critical values. Those properties uniquely determine the named…
Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves
Andrei Bogatyrev
For the evaluation and inversion of abelian integrals we show that the image of the Abel-Jacobi map of genus less than 5 hyperelliptic curve in its Jacobian is the intersection of…
Conformal mapping of rectangular heptagons
Andrei B. Bogatyrev
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.
Elementary construction of some Jenkins-Strebel differentials
Andrei Bogatyrev
We give an explicit multi-parametric construction for Jenkins-Strebel differentials on real algebraic curves. Roughly speaking, the square of any real holomorphic abelian different…
Rational functions admitting double decomposition
Andrei Bogatyrev
J.Ritt has investigated the structure of complex polynomials with respect to superposition. In particular, he listed all the polynomials admitting different double decompositions i…
Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations
Andrei Bogatyrev
Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete l…
Integral equations PS-3 and moduli of pants
Andrei Bogatyrev
More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems fo…