Infinite series identities from modular transformation formulas that stem from generalized Eisenstein series
Integrability of a linear center perturbed by a fourth degree homogeneous polynomial.
In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.
Intégration d'un système d'équations aux différentielles totales
Intégration, sous forme finie, de trois espèces d'équations différentielles linéaires, à coefficients variables.