Электронный каталог

Статья

Wang, S.
On the Behavior of Orbits of Vanhaecke System on Integral Surfaces / S.Wang, M.D.Malykh, L.A.Sevastianov, A.V.Zorin. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2026. – Vol. 34, No. 2. – P. 226-240. – URL: https://doi.org/10.22363/2658-4670-2026-34-2-226-240. – Bibliogr.: 21.

In the 1990s, P.Vanhecke described a Hamiltonian system with two degrees of freedom and a polynomialHamiltonian integrable in Abelian functions of two variables. This system provides a convenient example of anintegrable system (in the sense of Liouville) in which integral curves are wound on a two-dimensional manifold,an algebraic surface in a 4-dimensional phase space. We show that all necessary calculations can be performedin the Sage system. The results of numerical experiments performed in our package FDM for Sage are presented.It is shown that orbits of Vanhecke system can be divided into two classes, periodic and non-periodic. The pointsof the periodic orbits corresponding to solutions with the same period form an equiperiodic surface. Thereare infinitely many different algebraic equiperiodic surfaces. The behavior of nonperiodic orbits in numericalexperiments is determined not so much by the rationality or irrationality of the ratio of two periods of Abelianfunctions, but by the possibility of approximating this number with a rational fraction with high accuracy.



Спец.(статьи,препринты) = С 132 - Математический анализ
Спец.(статьи,препринты) = С 133.1 - Обыкновенные дифференциальные уравнения. Дифференциальные уравнения в частных производных. Обобщенные решения дифференциальных уравнений
ОИЯИ = ОИЯИ (JINR)2026