×

On first integrals of linear Hamiltonian systems. (English. Russian original) Zbl 1408.37099

Dokl. Math. 98, No. 3, 616-618 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 5, 482-484 (2018).
Summary: In the paper, Lax pairs for linear Hamiltonian systems of differential equations are found. Besides, first integrals of the system which are obtained from the Lax pairs are investigated.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] V. I. Arnold, Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1989; Springer-Verlag, New York, 1989).
[2] Kozlov, V. V., No article title, J. Appl. Math. Mech., 56, 803-809, (1992) · Zbl 0792.70014
[3] Kozlov, V. V., No article title, Regul. Chaotic Dyn., 23, 26-46, (2018) · Zbl 1400.37061
[4] Williamson, J., No article title, Am. J. Math., 58, 141-163, (1936) · JFM 63.1290.01
[5] Williamson, J., No article title, Am. J. Math., 62, 881-911, (1940) · JFM 66.0991.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.