Higher-Dimensional Integrable Newton Systems with Quadratic Integrals of Motion

DOI10.1111/1467-9590.00239zbMath1141.37349OpenAlexW2070937249MaRDI QIDQ3522169

Hans Lundmark

Publication date: 1 September 2008

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/1467-9590.00239

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)

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The equation \(X\nabla \text{det}X = \text{det}X\nabla \text{tr}X\), multiplication of cofactor pair systems, and the Levi-Civita equivalence problem ⋮ Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮ Projective dynamics and classical gravitation ⋮ From Jacobi problem of separation of variables to theory of quasipotential Newton equations ⋮ Multiplication of solutions for linear overdetermined systems of partial differential equations ⋮ Projective dynamics and first integrals ⋮ Killing tensors, warped products and the orthogonal separation of the Hamilton-Jacobi equation ⋮ Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems ⋮ An extended Hénon-Heiles system ⋮ Hamiltonian description of nonlinear curl forces from cofactor systems ⋮ Multiplication for solutions of the equation grad \(f = M\) grad \(g\) ⋮ Structural equations for a special class of conformal Killing tensors of arbitrary valence

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