2024/10/23 by Baranzini, Stefano, Canneori, Gian Marco, Terracini, Susanna
#34C25 #34D15 #47J30 #70F10 #81V45 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.17848
We seek periodic trajectories of a system of multiple mutually repelling electrons on a half-line, with an attractive nucleus sitting at the origin. We adopt a variational viewpoint and study critical points of the associated Lagrange-action functional, by means of a modified Lusternik-Schnirelmann theory for manifolds with boundary. Additionally, when the charges of the electrons tend to zero, we show that frozen planet orbits converge to segments of a brake orbit for a Kepler-type problem, establishing a strong analogy with the Schubart orbits of the gravitational n-body problem.