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I. Gaishun (2005)
Stability of linear Hamiltonian systems in total differentials with periodic coeficientsDifferential Equations, 41
ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 2, pp. 172–181. c Pleiades Publishing, Inc., 2006. Original Russian Text c I.V. Gaishun, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 2, pp. 159–167. ORDINARY DIFFERENTIAL EQUATIONS Stability and Strong Stability of Quasistationary Linear Hamiltonian Systems in Total Differentials with Periodic Coefficients I. V. Gaishun Institute of Mathematics, National Academy of Sciences, Minsk, Belarus Received July 7, 2005 DOI: 10.1134/S0012266106020030 INTRODUCTION Criteria for stability and strong stability of linear Hamiltonian systems in total differentials with periodic coefficients were obtained in [1, 2] in terms of spectral properties of monodromy matrices. However, these criteria are not constructive, since the computation of monodromy matrices is a rather difficult problem. In the present paper, we obtain necessary and sufficient stability conditions for stationary linear Hamiltonian systems in total differentials and conditions for the insensitivity of stability of such systems to small periodic perturbations of their coefficients preserving the total integrability and the Hamiltonian property (strong stability). Stability and strong stability tests are given in terms of the spectral characteristics of the coefficient matrices and hence can be verified by tools of linear algebra. By way of example, we analyze diagonal
Differential Equations – Springer Journals
Published: Mar 22, 2006
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