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Differential Equations, Vol. 41, No. 6, 2005, pp. 773–779. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 6, 2005, pp. 739–745. Original Russian Text Copyright c 2005 by Gaishun. ORDINARY DIFFERENTIAL EQUATIONS Strong Stability of Linear Hamiltonian Systems in Total Di erentials with Periodic Coecients I. V. Gaishun Institute of Mathematics, National Academy of Sciences, Minsk, Belarus Received December 15, 2004 1. INTRODUCTION In [1], Hamiltonian systems in total di erentials were de ned, and some of their properties were investigated. In particular, a stability criterion was obtained, and sucient conditions for stability robustness under small perturbations preserving the Hamiltonian property, total integrability, and periodicity were obtained for the case in which the system is linear and has periodic coecients. In the present paper, we prove necessary and sucient conditions for the strong stability (or stability robustness) of linear periodic Hamiltonian systems in total di erentials. These conditions are an analog of the well-known Krein{Gelfand{Lidskii theorem [2, p. 172]. Just as in [1], the spectrum of a commuting tuple of matrices and some related geometric notions are the main technique of analysis. Therefore, in addition to the results of [1], in Sections 2 and 3, we represent a number of
Differential Equations – Springer Journals
Published: Jul 27, 2005
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