Variational approach to the n-body problem

点击翻译按钮获取中文摘要

I proved the existence of periodic solutions with regularizable collisions in the n-body problem. This includes the proof of the existence of Schubart orbit with arbitrary masses in the collinear three-body problem, Broucke orbit in the isosceles three-body problem and Sekiguchi orbit in the symmetric collinear four-body problem. I also proved the existence of super-eight solution by using the variational method.We investigated the bifurcation phenomena on periodic solutions in the isosceles three-body problem.I proved the non-integrability of the collinear three-body problem by using the collision manifold theory.