Results 21 to 30 of about 267,752 (279)

Oscillation of linear Hamiltonian systems

Computers & Mathematics with Applications, 2002
The authors investigate oscillatory properties of the linear Hamiltonian system \[ x'=A(t)x+B(t)u,\quad u'=C(t)x-A^T(t)u, \tag{*} \] where \(A,B,C\) are \(n\times n\)-matrices with continuous entries for \(t\in [t_0,\infty)\), \(B,C\) are symmetric and the matrix \(B\) is supposed to be positive definite.
Meng, Fanwei, Sun, Yuangong
openaire   +2 more sources

Canonical transformations of linear Hamiltonian systems [PDF]

E3S Web of Conferences
In this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation ...
Titova Tatiana
doaj   +1 more source

Input-output decoupling of Hamiltonian systems: The linear case [PDF]

, 1985
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure.
Nijmeijer, H.
core   +3 more sources

Linear port-Hamiltonian DAE systems revisited

Systems & Control Letters, 2022
13 ...
Arjan van der Schaft, Volker Mehrmann
openaire   +4 more sources

Limit Cycles of Polynomially Integrable Piecewise Differential Systems

Axioms, 2023
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García, Jaume Llibre, Jesús S. Pérez del Río, Set Pérez-González   +3 more
doaj   +1 more source

Lax Pairs for Linear Hamiltonian Systems [PDF]

Siberian Mathematical Journal, 2019
In the paper Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Gr bner bases are used for the computations. It is proved that the maps which appear in the construction of Lax pairs are Poisson. Various properties of first integrals of the system which are obtained from the Lax pairs are investigated.
Zheglov, A. B., Osipov, D. V.
openaire   +3 more sources

Phase-Space Metric for Non-Hamiltonian Systems [PDF]

, 2005
We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion.
Dorfman J R, Dubrovin B A, Evans D J, Ezra G S, Ezra G S, Fomenko A N, Gerstenhaber M, Godbillon G, Helmholtz H, Hoover W G, Nose S, Sergi A, Sergi A, Suzuki M, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Trotter H F, Vasily E Tarasov   +20 more
core   +1 more source

Limit cycles of discontinuous piecewise linear differential systems formed by centers or Hamiltonian without equilibria separated by irreducible cubics

Moroccan Journal of Pure and Applied Analysis, 2021
The main goal of this paper is to provide the maximum number of crossing limit cycles of two different families of discontinuous piecewise linear differential systems.
Damene Loubna, Benterki Rebiha
doaj   +1 more source

Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Abstract and Applied Analysis, 2010
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋=ℝ and 𝕋=ℤ within ...
Shurong Sun, Martin Bohner, Shaozhu Chen
doaj   +1 more source

Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

Journal of Applied Mathematics, 2013
This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions
Yuan Shan, Baoqing Liu
doaj   +1 more source