The generalization of the Riccati equation studied in this work is z′(t) = z(t)n + an−1(t)z(t)n−1 + . . . + a1(t)z(t) + a0(t). The Advance Map takes za at zb if the initial value problem, with z(a) = za, has a solution defined on [a, b] with z(b) = zb. When a=0 and b=1 the Advance Map is known as Poincará Map. The singular set is the subset of the Riemann sphere containing the singularities of the advance map. In generic case, the singular set is the union of curves witha number finite discontinuities: corresponding solutions that reach infinity at least twice. As a consequence will be presented a method, based on configuration set singular, to determine the number of periodic solutions. A family of non-automous equations whose Poincaré Map is the Identity in a non-empty open subset of the complex plane will be presented.