SYMMETRIC PERIODIC ORBITS IN THREE SUB-PROBLEMS OF THE N-BODY PROBLEM

摘要

We study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of symmetric periodic orbits, including "Schubart-like" orbits and brake orbits, by using topological shooting arguments.