Geodesic
Analytic Dynamics of a One-Dimensional System of Particles with Strong Interaction
Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 262-275

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We consider the dynamics of a system of $N$ particles on the circle with interaction of nearest neighbors, a Coulomb potential, and an analytic external force. The trajectories are real analytic functions of time. However, the series for them converge only for sufficiently small times. For zero initial velocities and a uniform initial location of particles, we prove $N$-dependent estimates on the coefficients of this series.
Keywords: system of particles with strong interaction, electric current, analytic external force.
Mots-clés : Coulomb potential 
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     author = {V. A. Malyshev},
     title = {Analytic {Dynamics} of a {One-Dimensional} {System} of {Particles} with {Strong} {Interaction}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {92},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a7/}
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V. A. Malyshev. Analytic Dynamics of a One-Dimensional System of Particles with Strong Interaction. Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 262-275. http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a7/