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 Contemporary Mathematics and Its Applications: Year: Volume: Issue: Page: Find

 Contemporary Mathematics and Its Applications, 2016, Volume 100, Pages 58–75 (Mi cma407)

Transcendental first integrals of dynamical systems on the tangent bundle to the sphere

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In this paper, we examine the existence of transcendental first integrals for some classes of systems with symmetries. We obtain sufficient conditions of existence of first integrals of second-order nonautonomous homogeneous systems that are transcendental functions (in the sense of the theory of elementary functions and in the sense of complex analysis) expressed as finite combinations of elementary functions.

Full text: PDF file (234 kB)

English version:
Journal of Mathematical Sciences, 2017, 227:4, 442–460

Document Type: Article
UDC: 517.9+531.01

Citation: M. V. Shamolin, “Transcendental first integrals of dynamical systems on the tangent bundle to the sphere”, Contemporary Mathematics and Its Applications, 100 (2016), 58–75; Journal of Mathematical Sciences, 227:4 (2017), 442–460

Citation in format AMSBIB
\Bibitem{Sha16} \by M.~V.~Shamolin \paper Transcendental first integrals of dynamical systems on the tangent bundle to the sphere \jour Contemporary Mathematics and Its Applications \yr 2016 \vol 100 \pages 58--75 \mathnet{http://mi.mathnet.ru/cma407} \transl \jour Journal of Mathematical Sciences \yr 2017 \vol 227 \issue 4 \pages 442--460 \crossref{https://doi.org/10.1007/s10958-017-3596-9}