  In this paper we consider an attracting heteroclinic cycle made by a
1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles
having complex eigenvalues. The basin of the global attractor exhibits historic
behaviour and, from the asymptotic properties of these non-converging time
averages, we obtain a complete set of invariants under topological conjugacy in
a neighborhood of the cycle. These invariants are determined by the quotient of
the real parts of the eigenvalues of the equilibria, a linear combination of
their imaginary components and also the transition maps between two cross
sections on the separatrices.
