Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here, we argue in favor...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209443 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields / S. Klajbor-Goderich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862702251389222912 |
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| author | Klajbor-Goderich, S. |
| author_facet | Klajbor-Goderich, S. |
| citation_txt | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields / S. Klajbor-Goderich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here, we argue in favor of the usefulness of replacing an equivariant vector field by an isomorphic one to study the nonlinear stability of relative equilibria. In particular, we use this idea to obtain a criterion for nonlinear stability. As an application, we offer an alternative proof of Montaldi and Rodríguez-Olmos's criterion [arXiv:1509.04961] for the stability of Hamiltonian relative equilibria.
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| first_indexed | 2025-12-07T16:44:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209443 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:44:07Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Klajbor-Goderich, S. 2025-11-21T18:56:08Z 2018 Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields / S. Klajbor-Goderich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J25; 57R25; 37J15; 53D20 arXiv: 1707.02828 https://nasplib.isofts.kiev.ua/handle/123456789/209443 https://doi.org/10.3842/SIGMA.2018.021 We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here, we argue in favor of the usefulness of replacing an equivariant vector field by an isomorphic one to study the nonlinear stability of relative equilibria. In particular, we use this idea to obtain a criterion for nonlinear stability. As an application, we offer an alternative proof of Montaldi and Rodríguez-Olmos's criterion [arXiv:1509.04961] for the stability of Hamiltonian relative equilibria. The author would like to thank Eugene Lerman for guiding this project, for his enduring patience with my many questions, and for the many interesting conversations on the subject. The author would also like to express their gratitude to the anonymous referee for their helpful comments and careful review of the preprint of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields Article published earlier |
| spellingShingle | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields Klajbor-Goderich, S. |
| title | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields |
| title_full | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields |
| title_fullStr | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields |
| title_full_unstemmed | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields |
| title_short | Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields |
| title_sort | nonlinear stability of relative equilibria and isomorphic vector fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209443 |
| work_keys_str_mv | AT klajborgoderichs nonlinearstabilityofrelativeequilibriaandisomorphicvectorfields |