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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 028, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.028 (Mi sigma586) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Dynamical Studies of Equations from the Gambier Family

Partha Guhaa, Anindya Ghose Choudhuryb, Basil Grammaticoscd

a S. N. Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake, Calcutta-700098, India
b Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta-700009, India
c IMNC, Université Paris VII
d Paris XI, CNRS, UMR 8165, Bt. 104, 91406 Orsay, France
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DOI: https://doi.org/10.3842/SIGMA.2011.028
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.
Keywords: Gambier equation; Riccati sequence of differential equations; Milney–Pinney equation; folding transformation; superintegrability.
Received: December 10, 2010; in final form March 17, 2011; Published online March 22, 2011
Bibliographic databases:
Document Type: Article
MSC: 34C20; 70H05
Language: English
Citation: Partha Guha, Anindya Ghose Choudhury, Basil Grammaticos, “Dynamical Studies of Equations from the Gambier Family”, SIGMA, 7 (2011), 028, 15 pp.
Citation in format AMSBIB
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\paper Dynamical Studies of Equations from the Gambier Family
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