Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using decomposable Poisson structures. In the first case, the exist...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211630 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems. Misael Avendaño-Camacho, Claudio César García-Mendoza, José Crispín Ruíz-Pantaleón and Eduardo Velasco-Barreras. SIGMA 18 (2022), 038, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862629399660068864 |
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| author | Avendaño-Camacho, Misael García-Mendoza, Claudio César Ruíz-Pantaleón, José Crispín Velasco-Barreras, Eduardo |
| author_facet | Avendaño-Camacho, Misael García-Mendoza, Claudio César Ruíz-Pantaleón, José Crispín Velasco-Barreras, Eduardo |
| citation_txt | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems. Misael Avendaño-Camacho, Claudio César García-Mendoza, José Crispín Ruíz-Pantaleón and Eduardo Velasco-Barreras. SIGMA 18 (2022), 038, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using decomposable Poisson structures. In the first case, the existence of a Hamiltonian formulation is ensured under the vanishing of some topological obstructions, improving a result of Gao. In the second case, we apply a variant of the Hojman construction to solve the problem for vector fields admitting a transversally invariant metric and, in particular, for infinitesimal generators of proper actions. Finally, we also consider the hamiltonization problem for Lie group actions and give solutions in the particular case in which the acting Lie group is a low-dimensional torus.
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| first_indexed | 2026-03-14T17:46:21Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211630 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T17:46:21Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
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| spelling | Avendaño-Camacho, Misael García-Mendoza, Claudio César Ruíz-Pantaleón, José Crispín Velasco-Barreras, Eduardo 2026-01-07T13:41:22Z 2022 Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems. Misael Avendaño-Camacho, Claudio César García-Mendoza, José Crispín Ruíz-Pantaleón and Eduardo Velasco-Barreras. SIGMA 18 (2022), 038, 29 pages 1815-0659 2020 Mathematics Subject Classification: 37J06; 37J39; 53D17; 37C86; 70G45; 37C79 arXiv:2103.00458 https://nasplib.isofts.kiev.ua/handle/123456789/211630 https://doi.org/10.3842/SIGMA.2022.038 Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using decomposable Poisson structures. In the first case, the existence of a Hamiltonian formulation is ensured under the vanishing of some topological obstructions, improving a result of Gao. In the second case, we apply a variant of the Hojman construction to solve the problem for vector fields admitting a transversally invariant metric and, in particular, for infinitesimal generators of proper actions. Finally, we also consider the hamiltonization problem for Lie group actions and give solutions in the particular case in which the acting Lie group is a low-dimensional torus. We are very grateful to the anonymous referees for the observations and suggested improvements on various aspects of this work. This research was partially supported by the Mexican National Council of Science and Technology (CONACYT) under the grant CB2015 no. 258302 and the University of Sonora (UNISON) under the project no. USO315007338. J.C.R.P. thanks CONACyT for a postdoctoral fellowship held during the production of this work. E.V.B. was supported by FAPERJ grants E-26/202.411/2019 and E-26/202.412/2019. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems Article published earlier |
| spellingShingle | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems Avendaño-Camacho, Misael García-Mendoza, Claudio César Ruíz-Pantaleón, José Crispín Velasco-Barreras, Eduardo |
| title | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems |
| title_full | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems |
| title_fullStr | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems |
| title_full_unstemmed | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems |
| title_short | Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems |
| title_sort | geometrical aspects of the hamiltonization problem of dynamical systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211630 |
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