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A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems.
From a topological point of view, some...

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 Matematica (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 DEGREESn 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 Simo,...