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This article is cited in 1 scientific paper (total in 1 paper)
A one-parametric family of conformal mappings from the half-plane onto a family of polygons
I. A. Kolesnikov, A. Kh. Sharofov Tomsk State University
Abstract:
We consider a one-parametric family of conformal mappings from the upper half-plane onto the family of the polygons obtained by an angle-preserving shift of one or more vertices of some initial polygon. We obtain some differential equation for the family of mappings and some system of ordinary second-order differential equations for the preimages of the vertices of the family of polygons with Cauchy initial-value conditions.
Keywords:
conformal mapping, polygon, Schwarz–Christoffel integral.
Received: 23.03.2020 Revised: 05.05.2020 Accepted: 17.06.2020
Citation:
I. A. Kolesnikov, A. Kh. Sharofov, “A one-parametric family of conformal mappings from the half-plane onto a family of polygons”, Sibirsk. Mat. Zh., 61:5 (2020), 1027–1040; Siberian Math. J., 61:5 (2020), 818–829
Linking options:
https://www.mathnet.ru/eng/smj6034 https://www.mathnet.ru/eng/smj/v61/i5/p1027
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Abstract page: | 236 | Full-text PDF : | 106 | References: | 42 | First page: | 4 |
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