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TMF, 2018, Volume 197, Number 3, Pages 475–492 (Mi tmf9575)  

Discretization of Hamiltonian systems and intersection theory

A. V. Tsiganov

Saint Petersburg State University, St. Petersburg, Russia

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).


DOI: https://doi.org/10.4213/tmf9575

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English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1806–1822

Bibliographic databases:

Document Type: Article
PACS: 02.30.Ik
MSC: 37J35; 70H06
Received: 03.04.2018
Revised: 30.05.2018

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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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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