Integrability of Nonholonomic Heisenberg Type Systems

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
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dc.contributor.author	Grigoryev, Y. A.
dc.contributor.author	Sozonov, A.P.
dc.contributor.author	Tsiganov, A.V.
dc.date.accessioned	2019-02-18T14:53:57Z
dc.date.available	2019-02-18T14:53:57Z
dc.date.issued	2016
dc.identifier.citation	Integrability of Nonholonomic Heisenberg Type Systems / Y. A. Grigoryev, A.P. Sozonov, A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 37J60; 70G45; 70H45
dc.identifier.other	DOI:10.3842/SIGMA.2016.112
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148541
dc.description.abstract	We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical r-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.	uk_UA
dc.description.sponsorship	We are very grateful to the referees for thorough analysis of the manuscript, constructive suggestions and proposed corrections, which certainly lead to a more profound discussion of the results. We are also deeply grateful A.V. Borisov and I.A. Bizayev for the relevant discussion. Section 2 was written by A.V. Tsiganov and supported by the Russian Science Foundation (project 15-12-20035). Section 3 was written by Yu.A. Grigoryev and A.P. Sozonov within the framework of the Russian Science Foundation (project 15-11-30007).	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Integrability of Nonholonomic Heisenberg Type Systems	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA