Dynamical Studies of Equations from the Gambier Family

作者：Guha Partha^*; Choudhury Anindya Ghose; Grammaticos Basil

来源：Symmetry Integrability and Geometry-Methods and Applications, 2011, 7: 028.

DOI：10.3842/SIGMA.2011.028

• Gambier equation
• Riccati sequence of differential equations
• Milney-Pinney equation
• folding transformation
• superintegrability

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 Lienard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored.

• 出版日期2011