Contemporary Mathematics and Its Applications, Tome 100 (2016), pp. 58-75
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M. V. Shamolin. Transcendental first integrals of dynamical systems on the tangent bundle to the sphere. Contemporary Mathematics and Its Applications, Tome 100 (2016), pp. 58-75. http://geodesic.mathdoc.fr/item/CMA_2016_100_a5/
@article{CMA_2016_100_a5,
author = {M. V. Shamolin},
title = {Transcendental first integrals of dynamical systems on the tangent bundle to the sphere},
journal = {Contemporary Mathematics and Its Applications},
pages = {58--75},
year = {2016},
volume = {100},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMA_2016_100_a5/}
}
TY - JOUR
AU - M. V. Shamolin
TI - Transcendental first integrals of dynamical systems on the tangent bundle to the sphere
JO - Contemporary Mathematics and Its Applications
PY - 2016
SP - 58
EP - 75
VL - 100
UR - http://geodesic.mathdoc.fr/item/CMA_2016_100_a5/
LA - ru
ID - CMA_2016_100_a5
ER -
%0 Journal Article
%A M. V. Shamolin
%T Transcendental first integrals of dynamical systems on the tangent bundle to the sphere
%J Contemporary Mathematics and Its Applications
%D 2016
%P 58-75
%V 100
%U http://geodesic.mathdoc.fr/item/CMA_2016_100_a5/
%G ru
%F CMA_2016_100_a5
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.
