Geodesic
On the chaotization of one-dimensional gas consisting of interactive particles
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 393-399.

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We investigate the problem of motion of two identical particles on the unit segment. Particularly it was proved using the Poincaré method that in case of motion in any potential field one can find no additional first integrals except the full energy. W also found some conditions on the type potential under which the two-particles system is stable as the first approximation
Keywords: nonintegrability
Mots-clés : motion equations, billiard. 
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     title = {On the chaotization of one-dimensional gas consisting of interactive particles},
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P. A. Nagaev. On the chaotization of one-dimensional gas consisting of interactive particles. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 4, pp. 393-399. http://geodesic.mathdoc.fr/item/ND_2007_3_4_a1/