Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




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

Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 197, Number 3, Pages 475–492
DOI: https://doi.org/10.4213/tmf9575 (Mi tmf9575) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Discretization of Hamiltonian systems and intersection theory

A. V. Tsiganov

Saint Petersburg State University, St. Petersburg, Russia
Full-text PDF (573 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf9575
Abstract: We discuss the possibility of using the intersection points of the common level surface of integrals of motion with an auxiliary curve to construct finite-difference equations corresponding to different discretizations of the original integrable system. As an example, we consider the generalized one-dimensional oscillator with third- and fifth-degree nonlinearity, for which we show that the intersection divisors of the hyperelliptic curve with straight lines, quadrics, and cubics generate families of integrable discrete maps.
Keywords: finite-dimensional integrable system, discrete integrable map, intersection theory.
Funding agency Grant number
Russian Science Foundation 18-11-00032
This research was supported by a grant from the Russian Science Foundation (Project No. 18-11-00032).
Received: 03.04.2018
Revised: 30.05.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 197, Issue 3, Pages 1806–1822
DOI: https://doi.org/10.1134/S0040577918120103
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik
MSC: 37J35; 70H06
Language: Russian
Citation: A. V. Tsiganov, “Discretization of Hamiltonian systems and intersection theory”, TMF, 197:3 (2018), 475–492; Theoret. and Math. Phys., 197:3 (2018), 1806–1822
Citation in format AMSBIB
\Bibitem{Tsi18}
\by A.~V.~Tsiganov
\paper Discretization of Hamiltonian systems and intersection theory
\jour TMF
\yr 2018
\vol 197
\issue 3
\pages 475--492
\mathnet{http://mi.mathnet.ru/tmf9575}
\crossref{https://doi.org/10.4213/tmf9575}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3881814}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...197.1806T}
\elib{https://elibrary.ru/item.asp?id=36448188}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 197
\issue 3
\pages 1806--1822
\crossref{https://doi.org/10.1134/S0040577918120103}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000455189700010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059665718}
Linking options:
  • https://www.mathnet.ru/eng/tmf9575
  • https://doi.org/10.4213/tmf9575
  • https://www.mathnet.ru/eng/tmf/v197/i3/p475
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:356
    Full-text PDF :77
    References:54
    First page:16
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024