Topology of the configuration space, singularities of the potential, and polynomial integrals of equations of dynamics

DOI10.1070/SM8786zbMath1403.70009MaRDI QIDQ2957863

Valery V. Kozlov, Dmitrij V. Treshev

Publication date: 30 January 2017

Published in: Sbornik: Mathematics (Search for Journal in Brave)

zbMATH Keywords

order of singularitypolynomial integralsPoincaré conditionpotentials with singularities

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Topological and differential topological methods for problems in mechanics (70G40) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

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Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater, Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom, Small \(C^1\)-smooth perturbations of skew products and the partial integrability property, On integrability of dynamical systems, On momentum-polynomial integrals of a reversible Hamiltonian system of a certain form, Geometrically integrable maps in the plane and their periodic orbits, On quantum dynamics on \(C^\ast\)-algebras

Cites Work

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• The effect of singularities of the potential energy on the integrability of mechanical systems
• Ergodic and topological properties of coulombic periodic potentials
• Non-ergodicity of two particles interacting via a smooth potential
• Conservation laws of generalized billiards that are polynomial in momenta
• Potentials on the two-torus for which the Hamiltonian flow is ergodic