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First Approximation Formulas in the Problem of Perturbation of Definite and Indefinite Multipliers of Linear Hamiltonian Systems

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Abstract

New formulas of the first approximation are proposed in the problem of perturbing definite and indefinite multipliers of linear periodic Hamiltonian systems. The resultant formulas are based on the analysis of the spectral properties of the monodromy matrix system. The proposed formulas lead to new criteria according to the Lyapunov stability for linear periodic Hamiltonian systems in critical cases. Applications to the problem of parametric resonance in fundamental resonances are considered. The results obtained are formulated in terms of the original equations and brought to effective formulas and algorithms.

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Funding

The study of the third author was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (scientific topic code FZWU-2020-0027).

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Authors and Affiliations

  1. Bashkir State University, 450074, Ufa, Russia

    M. G. Yumagulov, L. S. Ibragimova & A. S. Belova

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  1. M. G. Yumagulov
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  2. L. S. Ibragimova
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  3. A. S. Belova
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Correspondence to M. G. Yumagulov, L. S. Ibragimova or A. S. Belova.

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(Submitted by T. K. Yuldashev)

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Yumagulov, M.G., Ibragimova, L.S. & Belova, A.S. First Approximation Formulas in the Problem of Perturbation of Definite and Indefinite Multipliers of Linear Hamiltonian Systems. Lobachevskii J Math 42, 3773–3783 (2021). https://doi.org/10.1134/S1995080222030222

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  • DOI: https://doi.org/10.1134/S1995080222030222

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