Recent Applications of the Theory of Lie Systems in Ermakov Systems
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149010 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Recent Applications of the Theory of Lie Systems in Ermakov Systems / J.F. Cariñena, J. de Lucas, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 52 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862661242326351872 |
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| author | Cariñena, J.F. de Lucas, J. Rañada, M.F. |
| author_facet | Cariñena, J.F. de Lucas, J. Rañada, M.F. |
| citation_txt | Recent Applications of the Theory of Lie Systems in Ermakov Systems / J.F. Cariñena, J. de Lucas, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 52 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation.
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| first_indexed | 2025-12-02T11:59:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149010 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T11:59:14Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cariñena, J.F. de Lucas, J. Rañada, M.F. 2019-02-19T12:56:34Z 2019-02-19T12:56:34Z 2008 Recent Applications of the Theory of Lie Systems in Ermakov Systems / J.F. Cariñena, J. de Lucas, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 52 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34A26; 34A05 https://nasplib.isofts.kiev.ua/handle/123456789/149010 We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). Partial financial support by research projects MTM2006-10531 and E24/1 (DGA) are acknowledged. JdL also acknowledge a F.P.U. grant from Ministerio de Educaci´on y Ciencia and a special grant from the Network of Mechanics, Geometry and Control. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Recent Applications of the Theory of Lie Systems in Ermakov Systems Article published earlier |
| spellingShingle | Recent Applications of the Theory of Lie Systems in Ermakov Systems Cariñena, J.F. de Lucas, J. Rañada, M.F. |
| title | Recent Applications of the Theory of Lie Systems in Ermakov Systems |
| title_full | Recent Applications of the Theory of Lie Systems in Ermakov Systems |
| title_fullStr | Recent Applications of the Theory of Lie Systems in Ermakov Systems |
| title_full_unstemmed | Recent Applications of the Theory of Lie Systems in Ermakov Systems |
| title_short | Recent Applications of the Theory of Lie Systems in Ermakov Systems |
| title_sort | recent applications of the theory of lie systems in ermakov systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149010 |
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