1. Departament de Matemàtiques , Universitat Autònoma de Barcelona , 08193 Bellaterra, Barcelona , Catalonia , Spain;2. Departamento de Matemàtica , Universidade Estadual de Campinas , Caixa Postal 6065, 13083-970, Campinas , SP , Brazil
Abstract:
We study the bifurcation of limit cycles from four-dimensional centres inside a class of polynomial differential systems. Our results establish an upper bound for the number of limit cycles which can be prolonged in function of the degree of the polynomial perturbation considered, up to first-order expansion of the displacement function with respect to small parameter. The main tool for proving such results is the averaging theory.