Date: 22/06/2026, 17:30
Location: Aula C13 Settore didattico Colombo M.
Speaker: Marta Dell'Atti (University of Warsaw)
Title: Systems with Painlevé transcendents in the coefficients free of movable critical points
Abstract: We construct a generalisation of what we call Bureau-Guillot systems: systems of first order equations with coefficient functions being Painlevé transcendents. The same Painlevé equation is related to the system and it appears as a regularising condition in the regularisation process. We extend the results of Bureau-Guillot considering polynomial systems free of movable critical points with degree larger than 2. These systems contain not only transcendents P-I and P-II in the coefficients, but also transcendents P-III, P-IV, P-V and P-VI (and/or their derivatives). We also present a simpler version of the change of variables to construct the analogues of the Bureau-Guillot systems in the "mixed" case: systems related to the equation P-J, with J=I, ..., VI, containing coefficient functions that are solutions to P-K with P-K ≠ P-J.
The talk is based on the joint work with G. Filipuk [1,2].
References
- M. Dell'Atti, G. Filipuk: Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence, Results Math. (2026)
- M. Dell'Atti, G. Filipuk: Generalisation of Bureau-Guillot systems with Painlevé transcendents in the coefficients, Preprint (2026).