Distribution and number of focal points for linear Hamiltonian systems

DOI10.1016/j.laa.2020.11.018zbMath1460.37082OpenAlexW3107334346MaRDI QIDQ2228482

Peter Šepitka, Roman Šimon Hilscher

Publication date: 17 February 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2020.11.018

zbMATH Keywords

linear Hamiltonian systemcomparative indexprincipal solutionright focal pointSturmian theoryleft focal point

Mathematics Subject Classification ID

Dynamical systems in control (37N35) Control/observation systems governed by ordinary differential equations (93C15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items

Generalized focal points and local Sturmian theory for linear Hamiltonian systems ⋮ Oscillation numbers for continuous Lagrangian paths and Maslov index ⋮ Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems ⋮ Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems

Cites Work

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• Comparison theorems for conjoined bases of linear Hamiltonian systems without monotonicity
• Symplectic difference systems: oscillation and spectral theory
• Disconjugacy
• Riccati differential equations
• Sturmian theory for linear Hamiltonian systems without controllability
• DEFINITENESS OF QUADRATIC FUNCTIONALS

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