43 citations · 123 across the 15 of their papers we have counts for
17 papers
A counterexample to the composition condition conjecture for polynomial Abel differential equations
Jaume Giné, Maite Grau, Xavier Santallusia
The Polynomial Abel differential equations are considered a model problem for the classical Poincaré center--focus problem for planar polynomial systems of ordinary differential eq…
Proving the existence of numerically detected planar limit cycles
Armengol Gasull, Héctor Giacomini, Maite Grau
This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré--Bendixson re…
Transversal conics and the existence of limit cycles
Héctor Giacomini, Maite Grau
This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré--Bendixson re…
Essential perturbations of polynomial vector fields with a period annulus
Adriana Buică, Jaume Giné, Maite Grau
In this paper we first give the explicit definition of essential perturbation. Secondly, given a perturbation of a particular family of centers of polynomial differential systems o…
Weierstrass integrability of differential equations
Jaume Giné, Maite Grau
The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterizatio…
A survey on the inverse integrating factor
Isaac A. García, Maite Grau
The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. F…