Torus knot choreographies in the n-body problem
DOI10.1088/1361-6544/abcb08zbMath1476.70035arXiv1901.03738OpenAlexW3173968493MaRDI QIDQ5147943
Jean-Philippe Lessard, Jason D. Mireles James, Carlos García-Azpeitia, Renato C. Calleja
Publication date: 29 January 2021
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.03738
delay differential equationscomputer-assisted proofscelestial mechanicscontraction mappingchoreographies
Fixed-point theorems (47H10) Periodic solutions to functional-differential equations (34K13) Periodic orbits of vector fields and flows (37C27) Celestial mechanics (70F15) Algorithms with automatic result verification (65G20) (n)-body problems (70F10) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)
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- Beyond the Melnikov method: A computer assisted approach
- Global bifurcation diagrams of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system
- Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
- Global bifurcation of polygonal relative equilibria for masses, vortices and dNLS oscillators
- Unchained polygons and the \(N\) -body problem
- Computational fixed-point theory for differential delay equations with multiple time lags
- A numerical verification method for a periodic solution of a delay differential equation
- Instabilities in the Sun-Jupiter-asteroid three body problem
- Variational proof of the existence of the super-eight orbit in the four-body problem
- Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space
- Heteroclinic connections between periodic orbits in planar restricted circular three body problem. II
- Stable periodic solutions for delay equations with positive feedback -- a computer-assisted proof
- Symmetric trajectories for the \(2N\)-body problem with equal masses
- A new branch of mountain pass solutions for the choreographical 3-body problem
- Symmetry groups of the planar three-body problem and action-minimizing trajectories
- Computer-assisted proofs in analysis
- Periodic solutions of analytic functional differential equations are analytic
- Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
- Binary decompositions for planar \(N\)-body problems and symmetric periodic solutions
- Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem
- Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
- Rigorous computer-assisted application of KAM theory: a modern approach
- A proof of Wright's conjecture
- A proof of Jones' conjecture
- Choreographies in the \(n\)-vortex problem
- Special issue on Hamiltonian systems and applications. Papers of the 4th international conference on dynamical systems and differential equations, Wilmington, UK, May 24--27, 2002.
- Computing discrete convolutions with verified accuracy via Banach algebras and the FFT.
- Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the \(n\)-body problem
- A complete proof of the Feigenbaum conjectures
- \(C^1\) Lohner algorithm.
- On the existence of collisionless equivariant minimizers for the classical \(n\)-body problem
- Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the \(n\)-body problem
- Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence
- A general method for computer-assisted proofs of periodic solutions in delay differential problems
- Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
- Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
- Stability and uniqueness of slowly oscillating periodic solutions to Wright's equation
- Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem
- Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
- Rigorous Numerics in Dynamics
- Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
- Transition tori in the planar restricted elliptic three-body problem
- A computer-assisted proof of universality for area-preserving maps
- On the dihedraln-body problem
- Validated Continuation for Equilibria of PDEs
- Global smooth solution curves using rigorous branch following
- A computer-assisted proof of the Feigenbaum conjectures
- The existence of simple choreographies for theN-body problem—a computer-assisted proof
- Braids in classical dynamics
- Continuation of solutions and studying delay differential equations via rigorous numerics
- Action minimizing orbits in then-body problem with simple choreography constraint
- Computer Assisted Existence Proofs of Lyapunov Orbits at $L_2$ and Transversal Intersections of Invariant Manifolds in the Jupiter--Sun PCR3BP
- Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight
- Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
- Existence of a Center Manifold in a Practical Domain around $L_1$ in the Restricted Three-Body Problem
- Rigorous Computation of the Global Dynamics of Integrodifference Equations with Smooth Nonlinearities
- ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
- A remarkable periodic solution of the three-body problem in the case of equal masses
- The family \(P_{12}\) of the three-body problem -- the simplest family of periodic orbits, with twelve symmetries per period
- New periodic solutions for Newtonian \(n\)-body problems with dihedral group symmetry and topological constraints