Exclusion of quadruple collisions in minimizers of the planar equal-mass N-body problem

DOI10.1016/j.jde.2021.03.043zbMath1476.70039OpenAlexW3150236651MaRDI QIDQ2020208

Duokui Yan, Rongchang Liu

Publication date: 23 April 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.03.043

zbMATH Keywords

periodic orbitN-body problemvariation methodquadruple collision

Mathematics Subject Classification ID

(n)-body problems (70F10) Collisions in celestial mechanics, regularization (70F16)

Cites Work

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• Classification of periodic orbits in the planar equal-mass four-body problem
• Quasiperiodic collision solutions in the spatial isosceles three-body problem with rotating axis of symmetry
• Spatial double choreographies of the Newtonian \(2n\)-body problem
• Finiteness of relative equilibria of the four-body problem
• On action-minimizing retrograde and prograde orbits of the three-body problem
• Four-body central configurations with some equal masses
• How the method of minimization of action avoids singularities
• On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
• Topological bifurcations of central configurations in the \(N\)-body problem
• New periodic orbits in the planar equal-mass five-body problem
• Simple choreographies of the planar Newtonian \(N\)-body problem
• Star pentagon and many stable choreographic solutions of the Newtonian 4-body problem
• Transitive decomposition of symmetry groups for the \(n\)-body problem
• Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses
• Multiple periodic orbits connecting a collinear configuration and a double isosceles configuration in the planar equal-mass four-body problem
• Removing collision singularities from action minimizers for the \(N\)-body problem with free boundaries
• Variational methods for the choreography solution to the three-body problem
• Convex four-body central configurations with some equal masses
• A Minimizing Property of Keplerian Orbits
• Shape space figure-8 solution of three body problem with two equal masses
• Minima of the action integral in the Newtonian problem of 4 bodies with equal masses: `Hip-hop' orbits
• A remarkable periodic solution of the three-body problem in the case of equal masses
• New periodic solutions for Newtonian \(n\)-body problems with dihedral group symmetry and topological constraints