Polynomial conservation laws for the Lorentz gas and the Boltzmann-Gibbs gas

DOI10.1070/RM9707zbMath1418.37090OpenAlexW2400359211MaRDI QIDQ2816815

Valery V. Kozlov

Publication date: 25 August 2016

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm9707

zbMATH Keywords

Lorentz gasKAM theoryBirkhoff billiardspolynomial integralelastic reflectionBoltzmann-Gibbs gastopological obstructions to integrability

Mathematics Subject Classification ID

Statistical mechanics of gases (82D05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Collision of rigid or pseudo-rigid bodies (70F35) Dynamical aspects of statistical mechanics (37A60) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Nearly integrable Hamiltonian systems, KAM theory (70H08)

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Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups ⋮ A locally integrable multi-dimensional billiard system ⋮ Near Tangent Dynamics in a Class of Hamiltonian Impact Systems ⋮ Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom ⋮ Degenerate billiards ⋮ Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane ⋮ On Local Integrability in Billiard Dynamics

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