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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146785 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639101312761856 |
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| author | Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| author_facet | Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-01T01:20:58Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146785 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T01:20:58Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Dynamical Studies of Equations from the Gambier Family Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| title | 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_short | Dynamical Studies of Equations from the Gambier Family |
| title_sort | dynamical studies of equations from the gambier family |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146785 |
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