5 papers
Modified Painlevé systems with meromorphic solutions for polynomial Hamiltonians of all degrees
Marta Dell'Atti, Thomas Kecker
We review non-autonomous Hamiltonian systems, polynomial in two dependent variables, with the property that all of their solutions are meromorphic functions in the complex plane. T…
Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials
Costanza Benassi, Marta Dell'Atti
This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials o…
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…
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 Painl…
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…