6 citations · 6 across the 6 of their papers we have counts for
6 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…
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…
Takasaki's rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations
Galina Filipuk, Alexander Stokes
We study a Hamiltonian system without the Painlevé property and show that it admits a kind of regularisation on a bundle of rational surfaces with certain divisors removed, general…
Relations between different Hamiltonian forms of the third Painlevé equation
Galina Filipuk, Adam Ligȩza, Alexander Stokes
In this paper we study different Hamiltonian systems with polynomial and rational Hamiltonians associated with the generic third Painlevé equation and present explicit birational t…
Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
Anton Dzhamay, Galina Filipuk, Alexander Stokes
In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlevé equation…
Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach
Anton Dzhamay, Galina Filipuk, Adam Ligȩza +1
It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique -- there are many v…