Dynamical Studies of Equations from the Gambier Family
We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146785 |
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| Zitieren: | Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. |
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Guha, P. Ghose Choudhury, A. Grammaticos, B. 2019-02-11T15:10:29Z 2019-02-11T15:10:29Z 2011 Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. 1815-0659 https://nasplib.isofts.kiev.ua/handle/123456789/146785 We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the consequence of introducing Okamoto's folding transformation which maps the reduced Gambier equation to a Liénard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored. This paper is a contribution to the Proceedings of the Conference “Integrable Systems and Geometry” (August 12–17, 2010, Pondicherry University, Puducherry, India). The full collection is available at http://www.emis.de/journals/SIGMA/ISG2010.html. We wish to thank Alfred Ramani for enlightening discussions and constant encouragements. Two of us (PG and BG) would like to thank K.M. Tamizhmani, organizer of the conference Geometry of Integrable Systems at Pondicherry, India, for the invitation and his kind hospitality. One of the authors (AGC) wishes to acknowledge the support provided by the S.N. Bose National Centre for Basic Sciences, Kolkata in the form of an Associateship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dynamical Studies of Equations from the Gambier Family Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dynamical Studies of Equations from the Gambier Family |
| spellingShingle |
Dynamical Studies of Equations from the Gambier Family Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| title_short |
Dynamical Studies of Equations from the Gambier Family |
| title_full |
Dynamical Studies of Equations from the Gambier Family |
| title_fullStr |
Dynamical Studies of Equations from the Gambier Family |
| title_full_unstemmed |
Dynamical Studies of Equations from the Gambier Family |
| title_sort |
dynamical studies of equations from the gambier family |
| author |
Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| author_facet |
Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the consequence of introducing Okamoto's folding transformation which maps the reduced Gambier equation to a Liénard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146785 |
| citation_txt |
Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. |
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2025-12-01T01:20:58Z |
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2025-12-01T01:20:58Z |
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