Tensor invariants and integration of differential equations

DOI10.1070/RM9866zbMath1439.37057MaRDI QIDQ5220201

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Publication date: 11 March 2020

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

zbMATH Keywords

rigid bodyKovalevskaya exponentsHamiltonian formGoryachev-Chaplygin systeminvariant 1-form

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Integrable cases of motion in rigid body dynamics (70E40) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (12)

Tensor invariants of geodesic, potential, and dissipative systems on tangent bundles of two-dimensional manifolds ⋮ Invariant volume forms of geodesic, potential, and dissipative systems on a tangent bundle of a four-dimensional manifold ⋮ Invariant forms of geodesic, potential, and dissipative systems on tangent bundles of finite-dimensional manifolds ⋮ Invariants of fifth-order homogeneous systems with dissipation ⋮ Small \(C^1\)-smooth perturbations of skew products and the partial integrability property ⋮ Non-uniform Kozlov–Treschev averagings in the ergodic theorem ⋮ Invariant volume forms of variable dissipation systems with three degrees of freedom ⋮ Obstructions to integrability of nearly integrable dynamical systems near regular level sets ⋮ Unnamed Item ⋮ Chaplygin ball in a solenoidal field ⋮ Geometrically integrable maps in the plane and their periodic orbits ⋮ New cases of integrability of systems of geodesics and potential and dissipative systems on tangent bundles of finite-dimensional manifolds

Cites Work

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• The Euler-Jacobi-Lie integrability theorem
• Integrability of Hamiltonian systems
• Tensor invariants of quasihomogeneous systems of differential equations, and the Kovalevskaya-Lyapunov asymptotic method
• Linear systems with a quadratic integral
• Resonances for Kovalevskaya exponents and their memory of some tensor laws of conservation
• Rigid body dynamics
• Global properties of Kovalevskaya exponents
• Linear Hamiltonian systems: quadratic integrals, singular subspaces and stability
• Dynamical systems X. General theory of vortices. Transl. from the Russian by A. V. Ovchinnikov
• On non-integrability of general systems of differential equations
• Dynamical systems with multivalued integrals on a torus
• On the Hamiltonian property of linear dynamical systems in Hilbert space
• Remarks on a Lie theorem on the integrability of differential equations in closed form
• Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method
• Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• COMPATIBLE POISSON BRACKETS ON LIE ALGEBRAS AND COMPLETENESS OF FAMILIES OF FUNCTIONS IN INVOLUTION
• A simple model of the integrable Hamiltonian equation
• Symmetries and regular behavior of Hamiltonian systems
• Linear Hamiltonian systems are integrable with quadratics
• Multi-Hamiltonian property of a linear system with quadratic invariant
• Topology of quasi-periodic functions on the plane
• On a theorem of Liouville concerning integrable problems of dynamics
• Necessary condition for the existence of algebraic first integrals
• Necessary condition for the existence of algebraic first integrals

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