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

In this paper we classify the centers, the cyclicity of its Hopf bifurcation and the isochronicity of the polynomial differential systems in R(2) of degree d >= 7 odd that in complex notation z = x + iy can be written as (z) over dot = (lambda + i)z + (z (z) over bar)(d-7/2) (Az(6)(z) over bar + Bz(4)(z) over bar (3) + Cz(2)(z) over bar (5) + D (z) over bar (7)), where lambda is an element of R, and A, B, C, D is an element of C.