2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80336The problem of two fixed centers is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral $G$. Some straightforward generalizations of the problem still have the generalization of $G$ as a first integral, but do not possess the energy integral. We present some numerical integrations suggesting that in the domain of bounded orbits the behavior of these {\it a priori} non hamiltonian systems is very similar to the behavior of usual quasi-integrable systems.4, 14, typos addedChaotic DynamicsExactly Solvable and Integrable Systemstext