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Dynamical Studies of Equations from the Gambier Family
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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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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Dynamical Studies of Equations from the Gambier Family
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
644
Завантажень:
267
Анотація:
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.
