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Matematicheskie Zametki, 2023, Volume 114, Issue 1, Pages 57–67
DOI: https://doi.org/10.4213/mzm13684 (Mi mzm13684) 		 
Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane

A. Vishnevskaya, M. V. Demina

HSE University, Moscow
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DOI: https://doi.org/10.4213/mzm13684
Abstract: The paper deals with the study of the model of point vortices proposed by the German scientist Hermann Helmholtz. Necessary and sufficient conditions for the existence of infinitely many nonequivalent stationary configurations are found for a system consisting of two point vortices of intensity $\Gamma_1$ and an arbitrary number of point vortices of intensity $\Gamma_2$. A classification of such configurations is carried out. For the first time, a connection is discovered between the negative Diophantine Pell equation and stationary configurations of point vortices on the plane.
Keywords: point vortex, infinite-dimensional configuration, stationary configuration, negative Pell equation.
Funding agency Grant number
Russian Science Foundation 19-71-10003
This work was financially supported by the Russian Science Foundation, project 19-71-10003, https://rscf.ru/en/project/19-71-10003/.
Received: 09.08.2022
Revised: 29.03.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 1, Pages 46–54
DOI: https://doi.org/10.1134/S0001434623070040
Bibliographic databases:
Document Type: Article
UDC: 517.926.4
MSC: 34M03; 76M40
Language: Russian
Citation: A. Vishnevskaya, M. V. Demina, “Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane”, Mat. Zametki, 114:1 (2023), 57–67; Math. Notes, 114:1 (2023), 46–54
Citation in format AMSBIB
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\by A.~Vishnevskaya, M.~V.~Demina
\paper Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 1
\pages 57--67
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\crossref{https://doi.org/10.4213/mzm13684}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4634770}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 1
\pages 46--54
\crossref{https://doi.org/10.1134/S0001434623070040}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85168599524}
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