Given a continuous or discrete dynamical system, it is natural to ask to what extent it can be identified by some of its orbits. The sytems considered in this talk are generated by "Dulac maps", which appear in various works dedicated to Hilbert's sixteen problem. A Dulac map is analytic on some open interval (0, d), and admits a non-trivial power-logarithmic asymptotic expansion at 0. We show that a convenient asymptotic analysis of the epsilon-neighborhood of one its orbits allows to determine the formal class of such a system. The proof involves various aspects of iteration theory, as well as several manipulations of transseries. Joint work with P. Mardesic, M. Resman and V. Zupanovic.