2018/07/12 by I. Hoveijn, Igor Hoveijn, H. Waalkens +5 · 1 citation
Mathematics · Physics and Astronomy · #37J15 #37J35 #53D20 #70F07 #70H33 #Black Holes and Theoretical Physics #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Quantum chaos and dynamical systems #math.DS #msc:37J15 #msc:37J35 #msc:53D20 #msc:70F07 #msc:70H33
paper · pdf · doi:10.48550/arxiv.1807.04522
37 pages, 5 figures
arxiv created 2018/07/12 · openalex publication_date 2018/07/12 · arxiv updated 2018/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of the map of integrals. Due to the non-compactness of the integral manifolds one has to take into account besides `ordinary' critical points also critical points at infinity. In the present paper we concentrate on `ordinary' critical points and in particular elucidate their connection to central configurations. In a second paper we will study critical points at infinity. The implications for the Hill regions, i.e. the projections of the integral manifolds to configuration space, are the subject of a third paper.