Integrability of Nonholonomic Heisenberg Type Systems
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 f...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148541 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862535183576596480 |
|---|---|
| author | Grigoryev, Y. A. Sozonov, A.P. Tsiganov, A.V. |
| author_facet | Grigoryev, Y. A. Sozonov, A.P. Tsiganov, A.V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-24T09:17:30Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148541 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T09:17:30Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Grigoryev, Y. A. Sozonov, A.P. Tsiganov, A.V. 2019-02-18T14:53:57Z 2019-02-18T14:53:57Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 37J60; 70G45; 70H45 DOI:10.3842/SIGMA.2016.112 https://nasplib.isofts.kiev.ua/handle/123456789/148541 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. 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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrability of Nonholonomic Heisenberg Type Systems Article published earlier |
| spellingShingle | Integrability of Nonholonomic Heisenberg Type Systems Grigoryev, Y. A. Sozonov, A.P. Tsiganov, A.V. |
| title | Integrability of Nonholonomic Heisenberg Type Systems |
| title_full | Integrability of Nonholonomic Heisenberg Type Systems |
| title_fullStr | Integrability of Nonholonomic Heisenberg Type Systems |
| title_full_unstemmed | Integrability of Nonholonomic Heisenberg Type Systems |
| title_short | Integrability of Nonholonomic Heisenberg Type Systems |
| title_sort | integrability of nonholonomic heisenberg type systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148541 |
| work_keys_str_mv | AT grigoryevya integrabilityofnonholonomicheisenbergtypesystems AT sozonovap integrabilityofnonholonomicheisenbergtypesystems AT tsiganovav integrabilityofnonholonomicheisenbergtypesystems |