id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-459	Barreira, Luis; Llibre, Jaume; Valls, Claudia	Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis	2020	14	.pdf	application/pdf	7017	309	74	Thus on the local chart U2 we obtain u′ = −3a12uv − 3a30u 3v − cu2v2 − αu4 − ω2 c v2, v′ = −v(a12v − a21x2 − 2a12xy − 3a03y 3 − 3αµx2y − αy3, ẏ = cx+ dy + 3a30x 2 + 2a21xy + a12y 2 + 3αµxy2. 6 L. BARREIRA, J. LLIBRE, C. VALLS EJDE-2020/57 Since this system must be invariant under the transformation (x, y, t) 7→ (x,−y,−t) we must have d = a21 = a03 = 0	cache/ejde-459.pdf	txt/ejde-459.txt