Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
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Publication:6155309
DOI10.1016/j.jde.2023.03.053zbMath1520.37058arXiv2205.03922OpenAlexW4366256699MaRDI QIDQ6155309
Jason D. Mireles James, Maciej J. Capiński, Shane Kepley
Publication date: 12 June 2023
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.03922
Three-body problems (70F07) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) Computer assisted proofs of proofs-by-exhaustion type (68V05)
Related Items (2)
Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four-body problem ⋮ Generalized analytical results on \(n\)-ejection-collision orbits in the RTBP. Analysis of bifurcations
Cites Work
- The parameterization method for invariant manifolds. From rigorous results to effective computations
- Global bifurcation of planar and spatial periodic solutions in the restricted \(n\)-body problem
- Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
- A numerical study of the orbits of second species of the planar circular RTBP
- Derived eigenvalues of symmetric matrices, with applications to distance geometry
- A new branch of mountain pass solutions for the choreographical 3-body problem
- Computer-assisted proofs in analysis
- Transversal ejection-collision orbits for the restricted problem and the Hill's problem with applications
- Numerical computation of heteroclinic orbits
- Triple collision in the planar isosceles three body problem
- Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study
- Triple collision in the collinear three-body problem
- Homoclinic orbits in Hamiltonian systems
- Triple collisions in the isosceles three body problem with small mass ratio
- Successive continuation for locating connecting orbits
- Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
- Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem
- Rigorous computer-assisted application of KAM theory: a modern approach
- Branches of periodic orbits for the planar restricted 3-body problem
- Global bifurcations of periodic solutions of the restricted three-body problem
- Continuation of periodic orbits in conservative and Hamiltonian systems
- Periodic and chaotic trajectories of the second species for the \(n\)-centre problem
- Quasiperiodic motions in the planar three-body problem
- \(C^1\) Lohner algorithm.
- Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem
- Topological bifurcations of central configurations in the \(N\)-body problem
- Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the \(n\)-body problem
- Symmetric regularization, reduction and blow-up of the planar three-body problem
- Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence
- Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set
- CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
- Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems
- Generalized analytical results on \(n\)-ejection-collision orbits in the RTBP. Analysis of bifurcations
- Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem
- Computer assisted proof of drift orbits along normally hyperbolic manifolds. II: Application to the restricted three body problem
- Computer-assisted estimates for Birkhoff normal forms
- Ejection-collision orbits in the RTBP
- Ejection-collision orbits in the symmetric collinear four-body problem
- Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
- Analytical and numerical results on families of \(n\)-ejection-collision orbits in the RTBP
- Transit regions and ejection/collision orbits in the RTBP
- Computer-assisted proofs in PDE: a survey
- Asymptotic density of collision orbits in the restricted circular planar 3 body problem
- Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem
- Nonplanar second species periodic and chaotic trajectories for the circular restricted three-body problem
- The parameterization method for invariant manifolds. III: Overview and applications
- The Krawczyk operator and Kantorovich's theorem
- High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem
- Dynamics and Mission Design Near Libration Points
- Consecutive quasi-collisions in the planar circular RTBP
- Rigorous Numerics in Dynamics
- Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system
- Verification methods: Rigorous results using floating-point arithmetic
- CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (II) : CYCLE-TO-CYCLE CONNECTIONS
- Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem
- The Numerical Computation of Connecting Orbits in Dynamical Systems
- Basics of regularization theory
- CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (I): POINT-TO-CYCLE CONNECTIONS
- Numerical continuation of families of homoclinic connections of periodic orbits in the RTBP
- A note on the existence of invariant punctured tori in the planar circular restricted three-body problem
- Transversal ejection-collision orbits in Hill's problem forC?1
- Triple collisions in the isosceles 3-body problem
- Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations
- A new regularization of the restricted three-body problem and an application
- The existence of simple choreographies for theN-body problem—a computer-assisted proof
- Dynamics and Mission Design Near Libration Points
- Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits
- Rigorous Numerics in Dynamics
- Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem
- Connecting orbits and invariant manifolds in the spatial restricted three-body problem
- On the restrited three-body problem when the mass parameter is small
- Improbability of Collisions in Newtonian Gravitational Systems. II
- Computer Assisted Existence Proofs of Lyapunov Orbits at $L_2$ and Transversal Intersections of Invariant Manifolds in the Jupiter--Sun PCR3BP
- Torus knot choreographies in the n-body problem
- Stationary Coexistence of Hexagons and Rolls via Rigorous Computations
- Computer-Assisted Proofs in Analysis and Programming in Logic: A case Study
- Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight
- On the construction of the Kolmogorov normal form for the Trojan asteroids
- TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS
- Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
- Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
- Existence of a Center Manifold in a Practical Domain around $L_1$ in the Restricted Three-Body Problem
- ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
- Erratum to "Improbability of Collisions in Newtonian Gravitational Systems"
- [https://portal.mardi4nfdi.de/wiki/Publication:5675367 Proof of a conjecture of E. Str�mgren]
- Averaging the planar three-body problem in the neighborhood of double inner collisions
- Global bifurcations of periodic solutions of the Hill lunar problem
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