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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)
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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
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    • 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
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