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 Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 1063–1100 (Mi izv1927)

The asymptotic behavior as $N\to\infty$ of the trajectories of $N$ point masses interacting in accordance with Newton's law of gravitation

V. P. Maslov, P. P. Mosolov

Abstract: For systems of particles interacting according to Newton's law of gravitation, the asymptotics of their trajectories are found. It is shown that these asymptotics are connected with the characteristics of Vlasov's equation, describing a collision-free plasma. An estimate of the difference between the trajectories of point masses and the corresponding characteristics of Vlasov's equation is found. It is proved that for small hydrodynamic times the motion of point masses is near to the motion of mass points in a constant field of force, defined by the initial mass distribution (the law of free fall). This law of free fall continues to hold when the particles pass through distances substantially exceeding the initial mutual distances between them.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 349–386

Bibliographic databases:

UDC: 517.9
MSC: 70F10, 76X05, 82A45

Citation: V. P. Maslov, P. P. Mosolov, “The asymptotic behavior as $N\to\infty$ of the trajectories of $N$ point masses interacting in accordance with Newton's law of gravitation”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1063–1100; Math. USSR-Izv., 13:2 (1979), 349–386

Citation in format AMSBIB
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\by V.~P.~Maslov, P.~P.~Mosolov
\paper The asymptotic behavior as $N\to\infty$ of the trajectories of~$N$ point masses interacting in accordance with Newton's law of gravitation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 1063--1100
\mathnet{http://mi.mathnet.ru/izv1927}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513914}
\zmath{https://zbmath.org/?q=an:0423.70011|0398.70008}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 349--386
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002047}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Maslov V., Shvedov O., “A New Asymptotic Method in the Problem of Many Classical Particles”, Dokl. Akad. Nauk, 338:2 (1994), 173–176
2. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122
3. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144
4. V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813
5. V. V. Vedenyapin, M. A. Negmatov, “Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form”, Theoret. and Math. Phys., 170:3 (2012), 394–405
6. V. V. Vedenyapin, M. A. Negmatov, “On derivation and classification of Vlasov type equations and equations of magnetohydrodynamics. The Lagrange identity, the Godunov form, and critical mass”, Journal of Mathematical Sciences, 202:5 (2014), 769–782
7. Vedenyapin V.V., Negmatov M.A., “On the Topology of Steady-State Solutions of Hydrodynamic and Vortex Consequences of the Vlasov Equation and the Hamilton–Jacobi Method”, Dokl. Math., 87:2 (2013), 240–244
8. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541
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