### Abstract

Recently some new connections have been found between the structure of the closed trajectories of plane systems of ODE's and certain questions in classical analysis and algebra. In particular, this concerns the vanishing problem of certain moment-like expressions and of iterated integrals on one side, and the structure of the composition factorization of analytic functions on the other. These connections provide a useful information on the Center conditions (for all the trajectories around a critical point to be closed) and on the distribution of the isolated closed trajectories (limit cycles). Some of the above effects are rather "structural" or "formal" in their nature, and, as the preliminary considerations show, they possibly can be considered in the framework of the Model Theory.