Geodesic
Integrable systems on tangent bundle of multi-dimensional sphere
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 60-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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The systems which have finite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tangent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimensional sphere under increase of its dimension and absence of force field is analyzed. At that, nonconservative fields of forces are presented with the presence of which the systems possess the complete choice of first integrals expressing in terms of finite combination of elementary functions and are, in general, the transcendental functions of its variables.
Keywords: dynamical system, integrability in terms of elementary functions, transcendental first integral. 
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N. V. Pokhodnya; M. V. Shamolin. Integrable systems on tangent bundle of multi-dimensional sphere. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 7 (2014), pp. 60-69. http://geodesic.mathdoc.fr/item/VSGU_2014_7_a4/

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[8] Trofimov V. V., “Symplectic structures on symmetruc spaces automorphysm groups”, Bulletin of Moscow University, 1984, no. 6, 31–33 (in Russian) | MR

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