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Funktsional'nyi Analiz i ego Prilozheniya, 2017, Volume 51, Issue 3, Pages 4–21
DOI: https://doi.org/10.4213/faa3478 (Mi faa3478) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications

T. Ayanoa, V. M. Buchstaberb

a Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/faa3478
Abstract: The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of its sigma function. As an application, solutions of the corresponding families of polynomial dynamical systems in $C^4$ with two polynomial integrals are constructed. These systems were introduced by Buchstaber and Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.
Keywords: Abelian functions, hyperelliptic sigma functions, polynomial dynamical systems, commuting vector fields, symmetric products of algebraic curves.
Received: 21.05.2017
Revised: 18.06.2017
Accepted: 26.05.2017
English version:
Functional Analysis and Its Applications, 2017, Volume 51, Issue 3, Pages 162–176
DOI: https://doi.org/10.1007/s10688-017-0181-4
Bibliographic databases:
Document Type: Article
UDC: 512.554.32+517.98
Language: Russian
Citation: T. Ayano, V. M. Buchstaber, “The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications”, Funktsional. Anal. i Prilozhen., 51:3 (2017), 4–21; Funct. Anal. Appl., 51:3 (2017), 162–176
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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