Tensor invariants of geodesic, potential, and dissipative systems on tangent bundles of two-dimensional manifolds

DOI10.1134/S1064562421060168zbMath1496.37062OpenAlexW4285336734MaRDI QIDQ2121851

M. V. Shamolin

Publication date: 5 April 2022

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

Full work available at URL: https://doi.org/10.1134/s1064562421060168

zbMATH Keywords

dissipationintegrabilitydynamical systeminvariant differential formtranscendental first integral

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (3)

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

Cites Work

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• Symplectic structures on groups of automorphisms of symmetric spaces
• Rational integrals of quasi-homogeneous dynamical systems
• New cases of integrable odd-order systems with dissipation
• New cases of homogeneous integrable systems with dissipation on tangent bundles of two-dimensional manifolds
• Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems
• Integrability and non-integrability in Hamiltonian mechanics
• On integrability in transcendental functions
• Tensor invariants and integration of differential equations
• Symmetry

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