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Polynomial conservation laws for the Lorentz gas and the Boltzmann-Gibbs gas. (English. Russian original) Zbl 1418.37090
Russ. Math. Surv. 71, No. 2, 253-290 (2016); translation from Usp. Mat. Nauk 71, No. 2, 81-120 (2016).

MSC:
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37A60 Dynamical aspects of statistical mechanics
37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
82D05 Statistical mechanics of gases
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
70F35 Collision of rigid or pseudo-rigid bodies
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70H08 Nearly integrable Hamiltonian systems, KAM theory
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