2021/07/11 by Kevin Constantineau, Constantineau, Kevin, Carlos García-Azpeitia +3 · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies
paper · pdf · doi:10.48550/arxiv.2107.05118
openalex publication_date 2021/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a classical model for the atom that considers the movement of n\ncharged particles of charge -1 (electrons) interacting with a fixed nucleus\nof charge \μ >0. We show that two global branches of spatial relative\nequilibria bifurcate from the n-polygonal relative equilibrium for each\ncritical values \μ =sk for k\∈ lbrack 2,...,n/2]. In these solutions,\nthe n charges form n/h-groups of regular h-polygons in space, where h\nis the greatest common divisor of k and n. Furthermore, each spatial\nrelative equilibrium has a global branch of relative periodic solutions for\neach normal frequency satisfying some nonresonant condition. We obtain\ncomputer-assisted proofs of the existence of several spatial relative\nequilibria on global branches away from the n-polygonal relative equilibrium.\nMoreover, the nonresonant condition of the normal frequencies for some spatial\nrelative equilibria is verified rigorously using computer-assisted proofs.\n