Central Configurations, Periodic Orbits, and Hamiltonian Systems

This book collects the notes of the lectures given in the Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School) held at Centre de Recerca Matemàtica (CRM) from January 27th to 31th, 2014. The notes consist of three series of lectures. One is dedicated to the study of periodic solutions of autonomous differential systems in R^n via the averaging theory, and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying central configurations. And the last one, given by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems.