56 citations · 289 across the 35 of their papers we have counts for
35 papers
On the discrete Painlevé equivalence problem, non-conjugate translations and nodal curves
Anton Dzhamay, Galina Filipuk, Alexander Stokes
We consider several examples of nonautonomous systems of difference equations coming from semi-classical orthogonal polynomials via recurrence coefficients and ladder operators, wi…
Generalisation of Bureau-Guillot systems with Painlevé transcendents in the coefficients
Marta Dell'Atti, Galina Filipuk
We construct a generalisation of what we call Bureau-Guillot systems, i.e. systems of first order equations with coefficient functions being Painlevé transcendents. The same Painle…
Iterative polynomial regularisation of PIV-type: Hamiltonian systems and Newton polygons
Marta Dell'Atti, Galina Filipuk
We study several polynomial Hamiltonian systems of PIV-type (including the mixed case quasi-PIV), and show that via the iterative process of polynomial regularisation, it is possib…
Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence
Marta Dell'Atti, Galina Filipuk
Bureau proposed a classification of systems of quadratic differential equations in two variables which are free of movable critical points, which was recently revised by Guillot. W…
The Painlevé equivalence problem for a constrained 3D system
Galina Filipuk, Michele Graffeo, Giorgio Gubbiotti +1
In this paper we propose a geometric approach to study Painlevé equations appearing as constrained systems of three first-order ordinary differential equations. We illustrate this…
Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation
Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar +1
We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities invol…