37 citations · 79 across the 13 of their papers we have counts for
6 papers · 1 filter
Discrete Painlevé Equations
Nalini Joshi
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlevé…
On the Riemann-Hilbert problem for a -difference Painlevé equation
Nalini Joshi, Pieter Roffelsen
A Riemann-Hilbert problem for a -difference Painlevé equation, known as , is shown to be solvable. This yields a bijective correspondence between the…
Re-factorising a QRT map
Nalini Joshi, Pavlos Kassotakis
A QRT map is the composition of two involutions on a biquadratic curve: one switching the -coordinates of two intersection points with a given horizontal line, and the other swi…
Classification of quad-equations on a cuboctahedron
Nalini Joshi, Nobutaka Nakazono
In this paper, we consider polynomials associated with faces and internal quadrilaterals of a cuboctahedron and classify them under the requirement that they are consistent. These…
A review of elliptic difference Painlevé equations
Nalini Joshi, Nobutaka Nakazono
Discrete Painlevé equations are nonlinear, nonautonomous difference equations of second-order. They have coefficients that are explicit functions of the independent variable an…
Elliptic asymptotics in -discrete Painlevé equations
Nalini Joshi, Elynor Liu
We study the asymptotic behaviour of two multiplicative- (-) discrete Painlevé equations as their respective independent variable goes to infinity. It is shown that the generic…