Spectral Analysis of Symplectic Matrices with Application to the Theory of Parametric Resonance

DOI10.1137/040618503zbMath1124.65040OpenAlexW2057181807MaRDI QIDQ5422462

Miloud Sadkane, Sergei Konstantinovich Godunov

Publication date: 22 October 2007

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/040618503

zbMATH Keywords

numerical exampleslinear Hamiltonian systemparametric resonancestrong stabilitysymplectic matrixspectral dichotomyspectral portrait

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Parametric resonances in linear vibration theory (70J40)

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Sergei Konstantinovich Godunov has turned 85 years old ⋮ Algorithm for separating matrix spectrum by an angle ⋮ First order structure-preserving perturbation theory for eigenvalues of symplectic matrices. II ⋮ METHOD OF SPECTRAL DICHOTOMY OF A MATRIX WITH RESPECT TO A CIRCLE OR AN ELLIPSE NOT CENTERED AT THE ORIGIN ⋮ First Order Structure-Preserving Perturbation Theory for Eigenvalues of Symplectic Matrices ⋮ Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations ⋮ On the strong stability of symplectic matrices ⋮ ON A PERTURBATION THEORY OF HAMILTONIAN SYSTEMS WITH PERIODIC COEFFICIENTS ⋮ A spectral trichotomy method for symplectic matrices

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