Topological classification of polynomial complex differential equations with all the critical points of centre type

In this paper, we study the global phase portrait of complex polynomial differential equations of degree n of the form ż = f(z), having all their critical points of centre type. We give the exact number of topologically different phase portraits on the Poincaré disk when n ≤ 6 and in the remaining cases, an upper bound for this number in terms of n. © 2010 Taylor & Francis.