Cubic Integrals of a Hamiltonian System with a $ C^{1} $ Potential on a Flat $ 2 $-Torus

Cubic Integrals of a Hamiltonian System with a $ C^{1} $ Potential on a Flat $ 2 $-Torus Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2026, Volume: 67, Number: 5, Pages: 1186-1202 Pages count : 17 DOI: 10.1134/s0037446626050186

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0026

We consider a two-dimensional Hamiltonian dynamical system with a potential periodic with respect to some lattice. If the system admits an integral F that is a polynomial of degree three in the momenta with coefficients periodic with respect to the same lattice, then it also admits an integral G linear in the momenta, and F is expressed in terms of G and the Hamiltonian H. For the integer lattice, this result was previously obtained by Bialy, while for an arbitrary lattice and an analytic potential it was obtained by Denisova and Kozlov. In the present paper, this assertion is proved for an arbitrary lattice and a potential of class C1. The proof becomes significantly more complicated.

Sharafutdinov V.A.
Cubic Integrals of a Hamiltonian System with a $ C^{1} $ Potential on a Flat $ 2 $-Torus
Siberian Mathematical Journal. 2026. V.67. N5. P.1186-1202. DOI: 10.1134/s0037446626050186 WOS Scopus OpenAlex

Шарафутдинов В.А.
Кубические интегралы гамильтоновой системы с потенциалом класса C1 на плоском 2-торе
Сибирский математический журнал. 2026. Т.67. №5. С.986-1006. DOI: 10.33048/smzh.2026.67.518 РИНЦ

Submitted:	Jun 3, 2026
Accepted:	Aug 11, 2026
Published print:	Sep 24, 2026
Published online:	Sep 24, 2026

≡ Web of science:	WOS:001885470600008
≡ Scopus:	2-s2.0-105051675857
≡ OpenAlex:	W7214181064