Time scale symplectic systems without normality

DOI10.1016/j.jde.2006.06.010zbMath1104.37037OpenAlexW2075886886MaRDI QIDQ855383

Vera Zeidan, Roman Šimon Hilscher

Publication date: 7 December 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.06.010

zbMATH Keywords

linear Hamiltonian systempositivityquadratic functionaltime scalenonnegativityconjoined basistime scale symplectic systemgeneralized focal point

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Discrete version of topics in analysis (39A12)

Related Items

Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases ⋮ Nabla time scale symplectic systems and related quadratic functionals ⋮ Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties ⋮ Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions ⋮ Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems ⋮ Sturmian theory for linear Hamiltonian systems without controllability ⋮ Applications of time scale symplectic systems without normality ⋮ Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems ⋮ Riccati equations for abnormal time scale quadratic functionals ⋮ Weyl-Titchmarsh theory for time scale symplectic systems on half line ⋮ Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter ⋮ Time scale embedding theorem and coercivity of quadratic functionals ⋮ Principal solutions at infinity for time scale symplectic systems without controllability condition ⋮ Picone type identities and definiteness of quadratic functionals on time scales

Cites Work

• Analysis on measure chains - a unified approach to continuous and discrete calculus
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• Matrix Lie theory and measure chains
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• Monotoneity Properties of Solutions of Hermitian Riccati Matrix Differential Equations
• Reid roundabout theorem for symplectic dynamic systems on time scales
• Quantum calculus
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