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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 1, Pages 39–56 (Mi zvmmf11013)  

This article is cited in 2 scientific papers (total in 2 papers)

Normal form of a Hamiltonian system with a periodic perturbation

A. D. Bruno

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Abstract: A perturbed Hamiltonian system with a time-independent unperturbed part and a time-periodic perturbation is considered near a stationary solution. First, the normal form of an autonomous Hamiltonian function is recalled. Then the normal form of a periodic perturbation is described. This form can always be reduced to an autonomous Hamiltonian function, which makes it possible to compute local families of periodic solutions of the original system. First approximations of some of these families are found by computing the Newton polyhedron of the reduced normal form of the Hamiltonian function. Computer algebra problems arising in these computations are briefly discussed.

Key words: Hamiltonian system, periodic perturbation, reduced normal form, families of periodic solutions.

DOI: https://doi.org/10.31857/S004446692001007X


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 36–52

Bibliographic databases:

UDC: 517.93
Received: 29.07.2019
Revised: 29.07.2019
Accepted:18.09.2019

Citation: A. D. Bruno, “Normal form of a Hamiltonian system with a periodic perturbation”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 39–56; Comput. Math. Math. Phys., 60:1 (2020), 36–52

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Batkhin, “Invariantnye koordinatnye podprostranstva normalnoi formy sistemy obyknovennykh differentsialnykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2020, 072, 23 pp.  mathnet  crossref
    2. Athanasios C. Tzemos, George Contopoulos, “Integrals of Motion in Time-periodic Hamiltonian Systems: The Case of the Mathieu Equation”, Regul. Chaotic Dyn., 26:1 (2021), 89–104  mathnet  crossref  mathscinet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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