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Oscillation results for linear Hamiltonian systems
Applied Mathematics and Computation, 2002The author considers linear Hamiltonian systems. He uses the generalized Riccati technique and establishes some new oscillation criteria of Philos and Kamenev types. The results improve some of the well-known results in the literature. Some examples are considered to illustrate the main results.
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Kinematic moment invariants for linear Hamiltonian systems
Physical Review Letters, 1990Summary: Quadratic moments of a particle distribution being transported through a linear Hamiltonian system are considered. A complete set of kinematic invariants made out of these moments are constructed leading to the discovery of new invariants.
Neri, Filippo, Rangarajan, Govindan
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Linearization of Hamiltonian and Gradient Systems
IMA Journal of Mathematical Control and Information, 1984Necessary and sufficient conditions are derived in order to transform a nonlinear Hamiltonian or gradient system by a change of coordinates of its state space into a linear Hamiltonian or gradient system. It is shown that such a transformaion necessarily respects the symplectic or metrical structure. The conditions are given in terms of the observation
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1990
Consider a system of m linear equations with continuous T -periodic coefficients: $$ \dot x = M\left( t \right)x $$ (1) where M (t) is a real m × m matrix, depending continuously on t ∈ ℝ such that: $$ M\left( {t + T} \right) = M\left( t \right) $$ (2) .
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Consider a system of m linear equations with continuous T -periodic coefficients: $$ \dot x = M\left( t \right)x $$ (1) where M (t) is a real m × m matrix, depending continuously on t ∈ ℝ such that: $$ M\left( {t + T} \right) = M\left( t \right) $$ (2) .
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Theorem on linearized Hamiltonian systems
Journal of Mathematical Physics, 1985Many nonlinear field equations can be written in Hamiltonian form. Thus the equation ∂tu=K(u) can be written ∂tu =[u, H], where H is an appropriate functional and [ , ] is a Poisson bracket. Frequently one is interested in the solution of the equation linearized about a given solution, i.e., the equation ∂t τ=K′(τ), where K′(τ)=(d/dε) K(u+ετ)‖ε=0.
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Regular Linear Hamiltonian Systems
2002Examination of systems of differential equations began in the early 1900’s with the work of G. D. Birkhoff and R. E. Langer (see [2] for example.), R. L. Wilder and L. Schlesinger. G. A. Bliss [3] in 1926 seems to have been the first to discuss regular, self-adjoint differential systems.
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Point Spectrum: Linear Hamiltonian Systems
2013Hamiltonian systems are about balance, with the energy and other invariants preserved under the flow. For a spatially localized critical point of a Hamiltonian system, the balance is reflected in the symmetry of the spectrum, which typically pins the essential spectrum to the imaginary axis in unweighted spaces.
Todd Kapitula, Keith Promislow
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General moment invariants for linear Hamiltonian systems
Physical Review A, 1992This paper studies the behavior of the moments of a particle distribution as it is transported through a Hamiltonian system. Functions of moments that remain invariant for an arbitrary linear Hamiltonian system are constructed. These functions remain approximately invariant for Hamiltonian systems that are not strongly nonlinear. Consequently, they can
, Dragt, , Neri, , Rangarajan
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Block Boundary Value Methods for linear Hamiltonian systems
Applied Mathematics and Computation, 1997The article continues the work of the authors on boundary value methods for the numerical integration of ordinary differential equations. Here they study the application of these methods to the symplectic integration of linear Hamiltonian systems. Compared with the standard approach to linear multistep methods [see e.g. \textit{T. Eirola} and \textit{J.
BRUGNANO, LUIGI, TRIGIANTE, DONATO
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Stability of linear almost-Hamiltonian periodic systems
Journal of Applied Mathematics and Mechanics, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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