Uspekhi Matematicheskikh Nauk
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 2021, Volume 76, Issue 4(460), Pages 37–104 (Mi umn10007)  

Surveys

Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves

V. M. Buchstabera, A. V. Mikhailovbc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b University of Leeds, Leeds, UK
c Centre of Integrable Systems, P.G. Demidov Yaroslavl State University

Abstract: This survey is devoted to integrable polynomial Hamiltonian systems associated with symmetric powers of plane algebraic curves. We focus our attention on the relations (discovered by the authors) between the Stäckel systems, Novikov's equations for the $g$th stationary Korteweg–de Vries hierarchy, the Dubrovin–Novikov coordinates on the universal bundle of Jacobians of hyperelliptic curves, and new systems obtained by considering the symmetric powers of curves when the power is not equal to the genus of the curve.
Bibliography: 52 titles.

Keywords: polynomial Hamiltonian systems, Stäckel systems, Korteweg–de Vries hierarchy, symmetric powers of curves, Abelian functions, systems of hydrodynamical type.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1397
EPSRC EP/V050451/1
The research of the second author was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation (contract no. 075-02-2021-1397) and the Engineering and Physical Sciences Research Council (grant no. EP/V050451/1).


DOI: https://doi.org/10.4213/rm10007

Full text: PDF file (957 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2021, 76:4, 587–652

Bibliographic databases:

UDC: 517.938+512.77
MSC: 14H70, 14K25, 37J35
Received: 10.05.2021

Citation: V. M. Buchstaber, A. V. Mikhailov, “Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves”, Uspekhi Mat. Nauk, 76:4(460) (2021), 37–104; Russian Math. Surveys, 76:4 (2021), 587–652

Citation in format AMSBIB
\Bibitem{BucMik21}
\by V.~M.~Buchstaber, A.~V.~Mikhailov
\paper Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves
\jour Uspekhi Mat. Nauk
\yr 2021
\vol 76
\issue 4(460)
\pages 37--104
\mathnet{http://mi.mathnet.ru/umn10007}
\crossref{https://doi.org/10.4213/rm10007}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4295018}
\elib{https://elibrary.ru/item.asp?id=47522338}
\transl
\jour Russian Math. Surveys
\yr 2021
\vol 76
\issue 4
\pages 587--652
\crossref{https://doi.org/10.1070/RM10007}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000712047200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85118700437}


Linking options:
  • http://mi.mathnet.ru/eng/umn10007
  • https://doi.org/10.4213/rm10007
  • http://mi.mathnet.ru/eng/umn/v76/i4/p37

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:155
    References:14
    First page:14

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022