Abstract

This project aims at the establishment of an investigation network between Brazil, Chile, France and Uruguay to promote the development of Mathematics in the areas of Hamiltonian Systems and Celestial Mechanics in these countries of South America. The main research topics are: central configuration in the N-body problem, integral manifolds in the gravitational N-body problem, central configurations, the stability of equilibrium solutions in Hamiltonian Systems, the existence and stability of periodic and quasi periodic solutions in Hamiltonian Systems and in particular to those derived from Celestial Mechanics, Non-integrability in Celestial Mechanics, Weak KAM solutions in the N-body problem, C⁰ and Lipschitz integrability for Tonelli Hamiltonians. It is worthwhile mentioning that this proposed scientific network involves a large number of young doctors as well as Master and PhD students in Mathematics. This project would facilitate the mobility of young doctors to make post-doctoral visits at the countries which are members of the network; also, Master students could eventually proceed to their doctoral studies in one of these countries. We intend to organize a one-week meeting in Uruguay, at the end of the 2017, and another one-week meeting in Recife, at the end of 2018. The goal is to promote discussions between the members of the cooperation network. These meeting are meant to stimulate the development of these emergent research centers as regards these topics of Mathematics.