7 papers
The space of initial conditions for linearisable mappings
T. Takenawa, M. Eguchi, B. Grammaticos +3
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisati…
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…
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…
The hunting for the discrete Painlevé VI is over
B. Grammaticos, A. Ramani
We present the discrete, q-, form of the Painlevé VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P…
On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
F. W. Nijhoff, A. Ramani, B. Grammaticos +1
A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painleve V equation. Its derivation is b…