The infinitesimal center problem concerns the persistence of a center under perturbations of a planar Hamiltonian differential system. Its first-order approximation is known as the tangential center problem. In this talk, we study the relationship between these two problems for systems whose origin is a non-degenerate center.

We introduce an algorithm that yields necessary conditions for the tangential center problem and explain how its solutions can be employed to investigate the infinitesimal center problem. As an illustration of the method, we present a family of cubic systems for which the tangential center problem admits a complete solution.