Linear Hamiltonian systems are integrable with quadratics

DOI10.1063/1.525330zbMath0507.70015OpenAlexW1986812583MaRDI QIDQ4745321

Hueseyin Kocak

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525330

zbMATH Keywords

normal formsimilarity transformationinfinitesimal symplectic matrixinto block diagonal formlinear Hamiltonian vector fieldnew proof of Williamson's theorem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Modal analysis in linear vibration theory (70J10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Canonical forms, reductions, classification (15A21) Free motions in linear vibration theory (70J30)

Related Items (14)

ON THE CONSTRUCTION OF TRANSFORMATIONS OF LINEAR HAMILTONIAN SYSTEMS TO REAL NORMAL FORMS ⋮ On the ergodic theory of equations of mathematical physics ⋮ A Jacobson–Morozov lemma for sp(2n, R) ⋮ Hypersurfaces in symplectic affine geometry. ⋮ First integrals and asymptotic trajectories ⋮ On linear equations of dynamics ⋮ Quadratic conservation laws for equations of mathematical physics ⋮ The Liouville equation as a Hamiltonian system ⋮ Lax pairs for linear Hamiltonian systems ⋮ Linear Hamiltonian systems: quadratic integrals, singular subspaces and stability ⋮ Tensor invariants and integration of differential equations ⋮ Multi-Hamiltonian property of a linear system with quadratic invariant ⋮ Topology and mechanics with computer graphics. Linear Hamiltonian systems in four dimensions ⋮ Quadratic integrals of linear Hamiltonian systems

Cites Work

• Conjugacy classes in linear groups
• On global action-angle coordinates
• An Algebraic Problem Involving the Involutory Integrals of Linear Dynamical Systems

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