New Periodic Solutions for Newtonian $n$-Body Problems with Dihedral Group Symmetry and Topological Constraints

Abstract

In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian $n$-body problems. In our assumption, the $n=2l\ge 4$ particles are invariant under the dihedral rotation group $D_l$ in ${\mathbb{R}}^3$ such that, at each instant, the $n$ particles form two twisted $l$-regular polygons. Our approach is variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.

References in corpus (2)

• Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry
• On the dihedral n-body problem

Cited by in corpus (1)

• Action minimizing orbits in the 2-center problems with simple choreography constraint