Almost stability of Hamilton's equations with quasiperiodic operator coefficients

V. N. Fomin


Abstract: This article studies a hamiltonian equation in Hilbert space which differs by only small quasiperiodic perturbations from equations with constant coefficients with several special properties. Necessary and sufficient conditions are obtained for strong formal stability of the hamiltonian equation with constant coefficients within some class of quasiperiodic perturbations. In the case of periodic perturbations, the result obtained allows us to extend to the class of equations studied here, the well known theorem of Krein, Gel'fand, and Lidskii on strong stability of hamiltonian systems.
Bibliography: 17 titles.

UDC: 517.43+513.881

MSC: 70H05, 70H09, 70H14, 70F15, 46C05

Received: 11.04.1968 and 18.04.1969

 English version: Mathematics of the USSR-Sbornik, 1970, 10:3, 289–306

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