On Strong Stability of Linear Poisson Actions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 5-12.

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Linear Poisson actions of the group Rm are considered. Conditions on the joint spectrum of the generators and on the centralizers assuring stability and strong stability of the action are given. We give also some examples of Poisson actions using CAS “Mathematica”.
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V. Glavan; Z. Rzeszótko. On Strong Stability of Linear Poisson Actions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 5-12. https://geodesic-test.mathdoc.fr/item/BASM_2003_2_a0/

[1] Meyer K. R., Hall G. R., Introduction to Hamiltonian dynamical systems and the $n$-body problem, Springer-Verlag, New York, 1992 | MR

[2] Cushman R., Kelly R., “Strongly stable real infinitesimal symplectic mappings”, J. Diff. Eq., 31:2 (1979), 200–223 | DOI | MR | Zbl

[3] Levi M., “On stability of symplectic maps”, J. Diff. Eq., 50:3 (1983), 441–443 | DOI | MR | Zbl

[4] Wójtkowski M. P., “A remark on strong stability of linear Hamiltonian systems”, J. Diff. Eq., 81:2 (1989), 313–316 | DOI | MR | Zbl

[5] Krein M. G., “Obobschenie nekotorykh issledovanii A. M. Lyapunova o lineinykh differentsialnykh uravneniyakh s periodicheskimi koeffitsientami”, DAN SSSR, 73:3 (1950), 445–448 | MR | Zbl

[6] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[7] Arnold V. I., Avez A., Les problemes ergodiques de la mechanique classique, Paris, 1967 | MR

[8] Gaishun I. V., Vpolne razreshimye mnogomernye differentsialnye uravneniya, Minsk, 1983 | MR

[9] Shcherbacov B. A., “The principle of composition of multidimensional dynamical systems”, Bul. AS RM, 1994, no. 1(14), 55–59 | MR

[10] Shcherbacov B. A., “Multidimensional dynamical systems”, Diff. Eq., 30:5 (1994), 679–686

[11] Lerman L. M., Umanskiy Ya. L., Four-dimensional integrable Hamiltonian systems with simple singular points (Topological aspects), Translations of Mathematical Monographs, 176, American Mathematical Society, Providence, 1998 | MR | Zbl

[12] Guralnick R. M., Sethuraman B. A., “Commuting pairs and triples of matrices and related varieties”, Linear Algebra Appl., 310 (2000), 139–148 | DOI | MR | Zbl

[13] Livšic M. S., Kravitsky N., Marcus A. S., Vinnikov V., Theory of commuting nonselfadjoint operators, Kluwer Academic Publishers, Dordrecht, 1995 | MR | Zbl

[14] Glavan V., “Strong stability criteria for the linear Hamilton-Pfaff systems”, Proceedings of the second international workshop on Mathematica system in teaching and research (Siedlce), Moscow, 2000

[15] Glavan V., Rzeszótko Z., “On strongly stable linear Poisson actions”, Treti nauchnye chteniya po obyknovennym differentsialnym uravneniyam (Minsk, Belarus, 2001)