Classical n-body scattering with long-range potentials
Résumé
We consider the scattering of n classical particles interacting via pair potentials, under the assumption that each pair potential is "long-range", i.e. being of order O(r −α) as r tends to infinity, for some α > 0. We define and focus on the "free region", the set of states leading to well-defined and well-separated final states at infinity. As a first step, we prove the existence of an explicit, global surface of section for the free region. This surface of section is key to proving the smoothness of the map sending a point to its final state and to establishing a forward conjugacy between the n-body dynamics and free dynamics. 1 Main results and setup 1.1 Main results Consider n classical particles moving in d-dimensional Euclidean space under the influence of a potential which is the sum of pair potentials. If the pair potentials die off appropriately at infinity then we expect that, within any widely separated fast-moving configuration of particles, the individual particles will move almost along straight lines. In this case it makes sense to talk about "scattering". See for example [DG, Sim, He, Hu1], and [Hu2]. We will prove new facts regarding
Domaines
Systèmes dynamiques [math.DS]
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