The Gambier Mapping

Abstract

We propose a discrete form for an equation due to Gambier and which belongs to the class of the fifty second order equations that possess the Painleve property. In the continuous case, the solutions of the Gambier equation is obtained through a system of Riccati equations. The same holds true in the discrete case also. We use the singularity confinement criterion in order to study the integrability of this new mapping.

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Cited by in corpus (10)

• Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
• The Gambier Mapping, Revisited
• Linearisable Mappings and the Low-Growth Criterion
• Integrable systems without the Painlevé property
• Singularity confinement and algebraic integrability
• Again, Linearizable Mappings
• Dynamical Studies of Equations from the Gambier Family
• Constructing Integrable Third Order Systems:The Gambier Approach
• Discrete systems related to some equations of the Painlevé-Gambier classification
• From Yang-Baxter maps to integrable quad maps and recurrences