Normal forms of symplectic matrices

DOI10.1007/s101140050005zbMath0959.15008OpenAlexW4249283750MaRDI QIDQ1578863

Di Dong, Long, Yiming

Publication date: 20 April 2001

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140050005

zbMATH Keywords

symplectic groupsperiodic solutionseigenvaluenormal formnonlinear Hamiltonian systemslinear Hamiltonian systemssymplectic matrixsymplectic transformationMaslov-type index theory

Mathematics Subject Classification ID

Related Items (9)

Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces ⋮ Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in \(\mathbb R^{2n}\) under a pinching condition ⋮ Normal forms for symplectic matrices ⋮ Index iteration theories for periodic orbits: old and new ⋮ The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Hyperbolic closed characteristics on compact convex smooth hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Topological structures of \(\omega\)-subsets in symplectic groups ⋮ Differentiable structure of \(\omega\)-subsets of symplectic groups

Cites Work

• Normal forms of symplectic pencils and the discrete-time algebraic Riccati equation
• Topological structures of \(\omega\)-subsets in symplectic groups
• Bott formula of the Maslov-type index theory
• A Maslov-type index theory for symplectic paths
• New aspects in the theory of stability of Hamiltonian systems
• Canonical forms for symplectic and Hamiltonian matrices
• The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
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