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The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients

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Topics in Differential and Integral Equations and Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 7))

Abstract

Let S be a mechanical system with m degrees of freedom whose Hamiltonian H has the form

$$H=\frac{1}{2}_\textrm{j},\sum_{\mathrm{k}=1}^{\mathrm{2m}}\mathrm{h_{jk}}(\omega \mathrm{t})\mathrm{x_jx_k}+\mathrm{f(t)},$$

where x1,...,xm are generalized coordinates, xm + 1,...,x2m are the corresponding generalized momenta of S, hjk(t) = hkj(t) (j,k = 1,...,m) are periodic functions of period T in the time variable t, and ω is a parameter.

Translation of: In Memory of A. A. Andronov, Izdat. Akad. Nauk. SSSR, Moscow (1955), 413-498.

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Authors
  1. M. G. Krein
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Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel

    I. Gohberg

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© 1983 Springer Basel AG

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Krein, M.G. (1983). The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients. In: Gohberg, I. (eds) Topics in Differential and Integral Equations and Operator Theory. Operator Theory: Advances and Applications, vol 7. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5416-0_1

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  • DOI: https://doi.org/10.1007/978-3-0348-5416-0_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5418-4

  • Online ISBN: 978-3-0348-5416-0

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