Limit cycles of resonant four-dimensional polynomial systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)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.252145158MEC/FEDER [MTM 2008-03437]CIRIT [2009SGR 410]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)MEC/FEDER [MTM 2008-03437]CIRIT [2009SGR 410]FAPESP [04/07386-2, 2007/06896-5