Dynamical Studies of Equations from the Gambier Family

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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dc.contributor.author	Guha, P.
dc.contributor.author	Ghose Choudhury, A.
dc.contributor.author	Grammaticos, B.
dc.date.accessioned	2019-02-11T15:10:29Z
dc.date.available	2019-02-11T15:10:29Z
dc.date.issued	2011
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146785
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Dynamical Studies of Equations from the Gambier Family	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA