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.
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
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\by A.~V.~Tsiganov
\paper Discretization of Hamiltonian systems and intersection theory
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\yr 2018
\vol 197
\issue 3
\pages 475--492
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\jour Theoret. and Math. Phys.
\yr 2018
\vol 197
\issue 3
\pages 1806--1822
\crossref{https://doi.org/10.1134/S0040577918120103}
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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:
Andrey V. Tsiganov, “Equivalent Integrable Metrics on the Sphere with Quartic Invariants”, SIGMA, 18 (2022), 094, 19 pp.
Alexey V. Borisov, Andrey V. Tsiganov, “On the Nonholonomic Routh Sphere in a Magnetic Field”, Regul. Chaotic Dyn., 25:1 (2020), 18–32
A. V. Tsiganov, “Discretization and superintegrability all rolled into one”, Nonlinearity, 33:9 (2020), 4924–4939
Chunmei Song, 2020 12th International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), 2020, 909
A. V. Tsiganov, “Superintegrable systems with algebraic and rational integrals of motion”, Theoret. and Math. Phys., 199:2 (2019), 659–674
A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
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