56 citations · 289 across the 35 of their papers we have counts for
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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…
Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities
Thomas Kecker, Galina Filipuk
In a 1979 paper, K. Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initia…