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Quasiinvariant deformations of invariant submanifolds of Hamiltonian dynamical systems

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Abstract

We study quasiinvariant deformations of invariant submanifolds of nonlinear Hamiltonian dynamical systems and their small perturbations.

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References

  1. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii,Soliton Theory: Inverse Problem Method [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. Yu. A. Mitropol'skii, N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, and V. G. Samoilenko,Integrable Dynamical Systems: Spectral and Differential Geometry Aspects [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  3. G. B. Whitham,Linear and Nonlinear Waves, Wiley, New York (1974).

    Google Scholar 

  4. A. K. Prikarpatskii and V. G. Samoilenko,Averaging Method and Equations of Ergodic Deformations for Nonlinear Evolution Equations [in Russian], Preprint No. 81.44, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1981).

    Google Scholar 

  5. A. K. Prikarpatskii and I. V. Mikityuk,Algebraic Aspects of Integrability of Nonlinear Dynamical Systems on Manifolds [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  6. A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  7. Z. Nitecki,Differentiable Dynamics. An Introduction to the Orbit Structure of Diffeomorphisms, MIT Press, Cambridge, London (1971).

    Google Scholar 

  8. Yu. A. Mitropol'skii, I. O. Antonishin, A. K. Prikarpatskii, and V. G. Samoilenko,Symplectic Analysis of Weakly Perturbed Dynamical Systems. A New Criterion of Stabilization of Homoclinic Separatrices and Its Application [in Ukrainian], Preprint No. 91.53, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).

    Google Scholar 

  9. V. K. Mel'nikov, “On the stability of a center under perturbations periodic in time,”Tr. Mosk. Mat. Obshch.,12, No. 1, 3–52 (1963).

    Google Scholar 

  10. H. Flaschka, M. G. Forest, and D. W. McLaughlin, “Multi-phase averaging and the inverse spectral solutions of the Kortewegde Vries equation,”Comm. Pure Appl. Math.,33, No. 6, 739–784 (1980).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. G. Samoilenko

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  1. V. G. Samoilenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1043–1054, August, 1994.

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Samoilenko, V.G. Quasiinvariant deformations of invariant submanifolds of Hamiltonian dynamical systems. Ukr Math J 46, 1145–1156 (1994). https://doi.org/10.1007/BF01056175

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  • DOI: https://doi.org/10.1007/BF01056175

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