Theoretical and Mathematical Physics

, Volume 197, Issue 3, pp 1806–1822 | Cite as

Discretization of Hamiltonian Systems and Intersection Theory

  • A. V. TsiganovEmail author


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.


finite-dimensional integrable system discrete integrable map intersection theory 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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