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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 C4 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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  • https://doi.org/10.4213/faa3478
  • https://www.mathnet.ru/eng/faa/v51/i3/p4
    • This publication is cited in the following 1 articles:
    1. Takanori Ayano, Victor M. Buchstaber, “Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3”, SIGMA, 15 (2019), 032, 15 pp.  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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