Oscillation numbers for continuous Lagrangian paths and Maslov index

DOI10.1007/s10884-022-10140-7zbMath1530.37087arXiv2107.01928OpenAlexW3178538698WikidataQ115382884 ScholiaQ115382884MaRDI QIDQ6132891

Julia V. Elyseeva, Peter Šepitka, Roman Šimon Hilscher

Publication date: 17 August 2023

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

Full work available at URL: https://arxiv.org/abs/2107.01928

zbMATH Keywords

Maslov indexsymplectic matrixcomparative indexLagrangian pathoscillation numberLidskii angle

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Lagrangian submanifolds; Maslov index (53D12) Analytic theory of partitions (11P82) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items

Generalized focal points and local Sturmian theory for linear Hamiltonian systems, Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems

Cites Work

• Unnamed Item
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• Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control
• Comparative index and Sturmian theory for linear Hamiltonian systems
• On symplectic transformations of linear Hamiltonian differential systems without normality
• Some remarks concerning weakly disconjugate linear Hamiltonian systems
• Comparative index for solutions of symplectic difference systems
• Comparison theorems for conjoined bases of linear Hamiltonian differential systems and the comparative index
• The Maslov index: A functional analytical definition and the spectral flow formula
• A limit theorem for monotone matrix functions
• The Maslov index and spectral counts for linear Hamiltonian systems on \([0, 1\)]
• Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and the comparative index
• Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
• Hörmander index in finite-dimensional case
• Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter
• On the Yakubovich frequency theorem for linear non-autonomous control processes
• Calculation of eigenvalues in a nonlinear spectral problem for the Hamiltonian systems of ordinary differential equations.
• Generalized inverses. Theory and applications.
• Comparative index and Lidskii angles for symplectic matrices
• Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
• Singular Sturmian comparison theorems for linear Hamiltonian systems
• Relative oscillation of linear Hamiltonian differential systems without monotonicity
• Comparison theorems for conjoined bases of linear Hamiltonian systems without monotonicity
• Distribution and number of focal points for linear Hamiltonian systems
• The comparative index and transformations of linear Hamiltonian differential systems
• The Maslov index for Lagrangian pairs on \(\mathbb{R}^{2 n}\)
• Nonautonomous linear-quadratic dissipative control processes without uniform null controllability
• Symplectic difference systems: oscillation and spectral theory
• Discrete and continuous boundary problems
• Hörmander's index and oscillation theory
• Rayleigh principle for linear Hamiltonian systems without controllability
• A modification of one method for solving nonlinear self-adjoint eigenvalue problems for hamiltonian systems of ordinary differential equations
• On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients
• On the maslov index
• Relative oscillation of linear Hamiltonian differential systems
• The Maslov and Morse indices for system Schroedinger operators on \mathBB{R}
• Index theory in nonlinear analysis
• The Maslov Index in Symplectic Banach Spaces
• Singular Sturmian separation theorems for nonoscillatory symplectic difference systems
• DEFINITENESS OF QUADRATIC FUNCTIONALS
• Renormalized oscillation theory for symplectic eigenvalue problems with nonlinear dependence on the spectral parameter
• A Generalized Index Theorem for Monotone Matrix-Valued Functions with Applications to Discrete Oscillation Theory
• Generalized Inverses of Linear Transformations
• Oscillatory properties of the solutions of canonical equations
• Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions
• Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter