TheN-body problem, the braid group, and action-minimizing periodic solutions
From MaRDI portal
Publication:4383955
DOI10.1088/0951-7715/11/2/011zbMath1076.70503OpenAlexW2056625485MaRDI QIDQ4383955
Publication date: 7 January 2003
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/11/2/011
Periodic solutions to ordinary differential equations (34C25) Braid groups; Artin groups (20F36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) (n)-body problems (70F10)
Related Items
Unnamed Item ⋮ Braids of the \(N\)-body problem. II: Carousel solutions by cabling central configurations ⋮ Periodic solutions of the planar \(N\)-center problem with topological constraints ⋮ On the variational approach to the periodic \(n\)-body problem ⋮ Triple collision orbits with nonzero initial velocities ⋮ A database of high precision trivial choreographies for the planar three-body problem ⋮ Braids, metallic ratios and periodic solutions of the \(2n\)-body problem ⋮ Periodic three-body orbits with vanishing angular momentum in the Jacobi–Poincaré ‘strong’ potential ⋮ Lissajous 3-braids ⋮ Angular Momentum and Topological Dependence of Kepler’s Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits ⋮ Existence of hyperbolic motions to a class of Hamiltonians and generalized \(N\)-body system via a geometric approach ⋮ On ``generalized Kepler's third law and mass dependence of periods of three-body orbits ⋮ Entire minimal parabolic trajectories: the planar anisotropic Kepler problem ⋮ Platonic polyhedra, topological constraints and periodic solutions of the classical \(N\)-body problem ⋮ New periodic solutions for some planar \(N + 3\)-body problems with Newtonian potentials ⋮ A guide to hunting periodic three-body orbits with non-vanishing angular momentum ⋮ Numerical verification of the microscopic time reversibility of Newton's equations of motion: fighting exponential divergence ⋮ Unnamed Item ⋮ Saari's homographic conjecture of the three-body problem ⋮ Some counterexamples to a generalized Saari’s conjecture ⋮ Platonic polyhedra, periodic orbits and chaotic motions in the \(N\)-body problem with non-Newtonian forces ⋮ Periodic solutions of theN-body problem with Lennard-Jones-type potentials ⋮ Braids of the N-body problem I: cabling a body in a central configuration ⋮ CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES ⋮ Action minimizers under topological constraints in the planar equal-mass four-body problem ⋮ Classical n-body scattering with long-range potentials ⋮ Non-planar minimizers and rotational symmetry in the \(N\)-body problem ⋮ A search for triple collision orbits inside the domain of the free-fall three-body problem ⋮ Application of Morse index in weak forceN-body problem ⋮ Simple choreographies of the planar Newtonian \(N\)-body problem ⋮ The zero angular momentum, three-body problem: All but one solution has syzygies ⋮ From brake to syzygy ⋮ Spatial double choreographies of the Newtonian \(2n\)-body problem ⋮ Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law: a numerical test ⋮ New periodic solutions for Newtonian \(n\)-body problems with dihedral group symmetry and topological constraints ⋮ Symmetry groups of the planar three-body problem and action-minimizing trajectories ⋮ Triple collision orbits in the free-fall three-body system without binary collisions ⋮ Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem ⋮ Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem ⋮ On action-minimizing retrograde and prograde orbits of the three-body problem ⋮ Topological fluid mechanics of point vortex motions
This page was built for publication: TheN-body problem, the braid group, and action-minimizing periodic solutions