143 citations · 921 across the 50 of their papers we have counts for
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Blending two discrete integrability criteria: singularity confinement and algebraic entropy
S. Lafortune, A. Ramani, B. Grammaticos +2
We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singularity, spontaneously appearing duri…
Discrete systems related to some equations of the Painlevé-Gambier classification
S. Lafortune, B. Grammaticos, A. Ramani +1
We derive integrable discrete systems which are contiguity relations of two equations in the Painlevé-Gambier classification depending on some parameter. These studies extend earli…
Linearisable systems and the Gambier approach
S. Lafortune, B. Grammaticos, A. Ramani
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show…
A Study of the Continuous and Discrete Gambier Systems
A. Ramani, B. Grammaticos, S. Lafortune
We present a systematic study of the Gambier system, which in the continuous case is given by two Riccati equations in cascade. We derive the condition for its integrability and sh…
Linearisable Mappings and the Low-Growth Criterion
A. Ramani, B. Grammaticos, S. Lafortune +1
We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confi…