Geodesic
Discretization of Hamiltonian systems and intersection theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 475-492
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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. 
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A. V. Tsiganov. Discretization of Hamiltonian systems and intersection theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 475-492. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a9/

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