Geodesic
Dynamical Studies of Equations from the Gambier Family
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Partha Guha; Anindya Ghose Choudhury; Basil Grammaticos. Dynamical Studies of Equations from the Gambier Family. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a27/

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