The existence of simple choreographies for theN-body problem—a computer-assisted proof

From MaRDI portal
Publication:4444051

DOI10.1088/0951-7715/16/6/302zbMath1060.70023arXivmath/0304404OpenAlexW1994376573MaRDI QIDQ4444051

Piotr Zgliczyński, Tomasz Kapela

Publication date: 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304404




Related Items (27)

On computer-assisted proving the existence of periodic and bounded orbitsAlgorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equationComet and moon solutions in the time-dependent restricted \((n+1)\)-body problemTransitive decomposition of symmetry groups for the \(n\)-body problemContinuation of normal doubly symmetric orbits in conservative reversible systemsRigorous KAM results around arbitrary periodic orbits for Hamiltonian systemsDistance estimates for action-minimizing solutions of the \(N\)-body problemChaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theoremComputer assisted proofs for transverse collision and near collision orbits in the restricted three body problemAnalytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error BoundsValidated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systemsBraids with the symmetries of Platonic polyhedra in the Coulomb (N+1)-body problemAn implicit algorithm for validated enclosures of the solutions to variational equations for ODEsTorus knot choreographies in the n-body problemAutomatic differentiation for Fourier series and the radii polynomial approachFinite resolution dynamicsSpatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existenceA computer-assisted proof of existence of a periodic solutionSimple choreographies of the planar Newtonian \(N\)-body problemOn the stability of periodic N-body motions with the symmetry of Platonic polyhedraSymmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the \(n\)-body problemA new branch of mountain pass solutions for the choreographical 3-body problemFrom the Lagrange polygon to the figure eight. I: Numerical evidence extending a conjecture of MarchalCAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systemsVariational proof of the existence of the super-eight orbit in the four-body problemA restricted four-body problem for the figure-eight choreographyLocal minimality properties of circular motions in \(1/r^\alpha\) potentials and of the figure-eight solution of the 3-body problem







This page was built for publication: The existence of simple choreographies for theN-body problem—a computer-assisted proof