Discretization of Hamiltonian Systems and Intersection Theory

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Discretization of Hamiltonian Systems and Intersection Theory. / Tsiganov, A. V.

In: Theoretical and Mathematical Physics(Russian Federation), Vol. 197, No. 3, 01.12.2018, p. 1806-1822.

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Author

Tsiganov, A. V. / Discretization of Hamiltonian Systems and Intersection Theory. In: Theoretical and Mathematical Physics(Russian Federation). 2018 ; Vol. 197, No. 3. pp. 1806-1822.

BibTeX

@article{cfe100d0289c4090b08e6bdadd2fb429,

title = "Discretization of Hamiltonian Systems and Intersection Theory",

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 = "discrete integrable map, finite-dimensional integrable system, intersection theory",

author = "Tsiganov, {A. V.}",

year = "2018",

month = dec,

day = "1",

doi = "10.1134/S0040577918120103",

language = "English",

volume = "197",

pages = "1806--1822",

journal = "Theoretical and Mathematical Physics (Russian Federation)",

issn = "0040-5779",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Discretization of Hamiltonian Systems and Intersection Theory

AU - Tsiganov, A. V.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - discrete integrable map

KW - finite-dimensional integrable system

KW - intersection theory

UR - http://www.scopus.com/inward/record.url?scp=85059665718&partnerID=8YFLogxK

U2 - 10.1134/S0040577918120103

DO - 10.1134/S0040577918120103

M3 - Article

AN - SCOPUS:85059665718

VL - 197

SP - 1806

EP - 1822

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -

ID: 37502098