Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torusстатья
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 20 мая 2017 г.
Аннотация:We consider dynamical systems with two degrees of freedom whose configuration space is a torus and which admit first integrals polynomial in velocity. We obtain constructive criteria for the existence of conditional linear and quadratic integrals on the two-dimensional torus. Moreover, we show that under some additional conditions the degree of an “irreducible” integral of the geodesic flow on the torus does not exceed 2.