Functional Analysis and Its Applications

, Volume 48, Issue 4, pp 242–249 | Cite as

Finding the incomplete Belitskii normal form of a Hamiltonian system

  • V. V. Basov
  • A. S. Vaganyan


We suggest an efficient method for finding the incomplete Belitskii normal form of a Hamiltonian system with many degrees of freedom and with a quasihomogeneous unperturbed part of special form. In particular, we obtain closed-form expressions for the incomplete Belitskii normal forms of two-degree-of-freedom Hamiltonian systems with unperturbed Hamiltonian of the form \(h_1 x_1^{l_1 } y_1^{m_1 } + h_2 x_2^{l_2 } y_2^{m_2 } \).

Key words

incomplete Belitskii normal form Hamiltonian system 


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  1. [1]
    G. R. Belitskii, “Invariant normal forms of formal series,” Funkts. Anal. Prilozhen., 13:1 (1979), 59–60; English transl.: Functional Anal. Appl., 13:1 (1979), 46–47.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    G. R. Belitskii, “Normal forms relative to the action of a group on a space,” Izv. Akad. Nauk SSSR, Ser. Matem., 41:5 (1977), 1053–1063; English transl.: Math. USSR Izv., 11:5 (1977), 1001–1010.MATHGoogle Scholar
  3. [3]
    V. V. Basov and A. S. Vaganyan, “Normal forms of Hamiltonian systems,” Differential Equations and Control Processes, 2010, No. 4, 86–107 (electronic journal Scholar
  4. [4]
    G. D. Birkhoff, Dynamical Systems, Colloquium Publications, vol. 9, Amer. Math. Soc., Providence, RI, 1927, 1966.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St.-Petersburg State UniversitySt.-PetersburgRussia

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