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Proof of Simultaneous Conditional Exponential Stabilization and Destabilization of Linear Hamiltonian Systems

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Abstract

It is proved that any linear Hamiltonian system is simultaneously conditionally (with respect to a subspace of half dimension) exponentially stabilizable and destabilizable by uniformly small Hamiltonian perturbations.

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References

  1. V. I. Arnol’d, Mathematical Method of Classic Mechanics (Editorial URSS, Moscow, 2000) [in Russian].

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  2. B. P. Demidovich, Lectures on Mathematical Stability Theory (Nauka, Moscow, 1967) [in Russian].

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  3. I. N. Sergeev, “To the Theory of Lyapunov Exponents of Linear Systems of Differential Equations,” Trudy Semin. I. G. Petrovskogo, No. 9, 111 (1983).

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  4. T. V. Salova, “On the Simultaneous Conditional Stabilizability and Destabilizability of Linear Hamiltonian Systems,” Differ. Uravn. 50 (12), 1676 (2014) [Differ. Equations 50 (12), 1681 (2014)].

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  5. T. V. Salova, “The Proof of Simultaneous Conditional Stabilization and Destabilization of Linear Hamiltonian Systems.” Vestn. Mosk. Univ. Matem. Mekhan., No. 6, 8 (2017).

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  6. T. V. Salova, “Simultaneous Attainability of Central Exponents of Four-Dimensional Hamiltonian Systems Under Infinitesimal Hamiltonian Perturbations,” Differ. Uravn. 50 (11), 1441 (2014) [Differ. Equations 50 (11), 1435 (2014)].

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    T. V. Salova

Authors
  1. T. V. Salova
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Correspondence to T. V. Salova.

Additional information

Original Russian Text © T.V. Salova, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 4, pp. 65–68.

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Salova, T.V. Proof of Simultaneous Conditional Exponential Stabilization and Destabilization of Linear Hamiltonian Systems. Moscow Univ. Math. Bull. 73, 168–170 (2018). https://doi.org/10.3103/S0027132218040095

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  • DOI: https://doi.org/10.3103/S0027132218040095

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