New periodic solutions for some planar N+3-body problems with Newtonian potentials

Abstract

For some planar Newtonian N +3-body problems, we use variational minimization methods to prove the existence of new periodic solutions satisfying that N bodies chase each other on a curve, and the other 3 bodies chase each other on another curve. From the definition of the group action in equations (3.1) − (3.3), we can find that they are new solutions which are also different from all the examples of Ferrario and Terracini (2004) [22].