Research objectives and content
program. The general scientific objectif are singularities of foliations, researchers. The teams in the network produce each year around ten Ph.D. dynamical systems or more general differential equations over the real or each of them gets easily a permanent position. The total amount of the budget directly devoted to the training of young people is around 1/3 of complex numbers. There are three main lines of work: reduction of singularities, differential Galois theory and geometry of the the total requested financement. The external (inside Europe) relations, as well as the amount of young researchers involved in the network, singularities. guarantees the existence of young researchers to be trained. The main tools we use are deformations, singular perturbations, group actions as group of diffeomorphisms, local algebra, cohomological methods, differential algebra and asymptotic developments. The proposed network is composed by seven teams with a big amount of previous scientifical connections and work in common on the proposed objectives. Many of the basic results in that directions come from join works of team's members.