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arXiv · 2608.29694

First integrals of dense hard-ball gases

Gleb Smirnov
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Abstract

We answer two questions of Kozlov about polynomial-in-momentum first integrals of billiard systems. For billiards in bounded polytopes, such integrals are independent of position. For hard-ball gases in a rectangular box, every polynomial-in-momentum first integral is a polynomial in the total kinetic energy whenever the collision graph is connected.

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Gleb Smirnov. 2026-08-30. First integrals of dense hard-ball gases. https://arxiv.org/abs/2608.29694

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