Classification of centers, their cyclicity and isochronicity for a class of polynomial differential systems of degree d ≥ 7 odd

摘要

In this paper we classify the centers, the cyclicity of its Hopf bifurcation and the isochronicity of the polynomial differential systems in ?~2 of degree d ≥ 7 odd that in complex notation z = x + iy can be written as ? = (λ + i)z + (z?)~(d-7/2) (Az~6Z? + Bz~4z?~3 + Cz ~2Z?~5 + Dz?~7), where λ ∈ ?, and A, B, C, D ∈ C.