2004/04/28 by Vivina Barutello, Barutello, Vivina, Davide L. Ferrario +3
Engineering · Mathematics · Physics and Astronomy · #37C80 #70F10 #70G75 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #math-ph #math.DS #math.MP #msc:37C80 #msc:70F10 #msc:70G75
paper · pdf · doi:10.48550/arxiv.math/0404514
LaTeX file, 36 pages; 11 figures. New abstract, some typos fixed A missing hypothesis added
openalex publication_date 2004/04/28 · arxiv created 2008/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of the equivariant calculus of variations. First, we show that symmetry groups of the Lagrangian action functional can be reduced to groups in a finite explicitly given list, after a suitable change of coordinates. Then, we show that local symmetric minimizers are always collisionless, without any assumption on the group other than the fact that collisions are not forced by the group itself. Moreover, we describe some properties of the resulting symmetric collisionless minimizers (Lagrange, Euler, Hill-type orbits and Chenciner--Montgomery figure-eight).