On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation

On some open problems in planar differential systems and Hilbert’s 16th problem

“…In [125] it was shown that H(3) P 12 and is the best result, so far, on the number of limit cycles for cubic systems. In the last few years different results have been obtained, for instance H(4) P 15, H(5) P 23 and H(6) P 35, see [115,120,121,128] and references therein.…”

On the number of limit cycles of a Z4-equivariant quintic polynomial system

“…Yu et al [8] proved that a cubic Z 3 -equivariant system can have three small limit cycles and one big limit cycle. Wu et al [9] studied a Z 4 -equivariant quintic system having at least 16 limit cycles. Zhang et al [10] found a quartic system having at least 15 limit cycles.…”

Limit cycles of a Z3-equivariant near-Hamiltonian system

“…Many studies had been done for planar systems close to Hamiltonian systems, especially for quadratic and cubic systems (see [6][7][8][9][10][11][12][13][14][15][16][17]). The main results are on the number of limit cycles which appear near a center, a periodic annular or a homoclinic loop by perturbations.…”