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Computer Assisted Proofs for Transverse Collision and Near Collision Orbits in the Restricted Three Body Problem

https://doi.org/10.2139/ssrn.4671783
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INTLAB — INTerval LABoratory
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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
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Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem
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Triple collisions in the isosceles three body problem with small mass ratio
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Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study
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Proof of a conjecture of E. Str�mgren
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On the restrited three-body problem when the mass parameter is small
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A new regularization of the restricted three-body problem and an application
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Transversal ejection-collision orbits in Hill's problem forC?1
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Triple collision in the planar isosceles three body problem
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Triple collision in the collinear three-body problem
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Sur la régularisation du problème des trois corps
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Periodic Orbits
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Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem
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Periodic Orbits, Symbolic Dynamics and Topological Entropy for the Restricted 3-Body Problem
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Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three-Body Problem - A Computer Assisted Proof
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A New Branch of Mountain Pass Solutions for the Choreographical 3-Body Problem
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Generalized Analytical Results on n-Ejection–Collision Orbits in the RTBP. Analysis of Bifurcations
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Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach
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C1 Lohner Algorithm
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Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem
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A numerical study of the orbits of second species of the planar circular RTBP
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Global bifurcation of planar and spatial periodic solutions in the restricted n-body problem
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Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem
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Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence
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Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set
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Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems
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Computer-assisted proofs in PDE: a survey
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Homoclinic orbits in Hamiltonian systems
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Transversal ejection-collision orbits for the restricted problem and the Hill's problem with applications
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The Krawczyk operator and Kantorovich's theorem
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Numerical computation of heteroclinic orbits
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Computer-assisted proofs in analysis
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Ejection-collision orbits in the RTBP
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Ejection-Collision orbits in the symmetric collinear four–body problem
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Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
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Analytical and numerical results on families of n-ejection-collision orbits in the RTBP
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Transit regions and ejection/collision orbits in the RTBP
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CAPD::DynSys: A flexible C++ toolbox for rigorous numerical analysis of dynamical systems
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High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem
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The parameterization method for invariant manifolds III: overview and applications
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Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the n-body problem
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Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem
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Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem
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Topological bifurcations of central configurations in the -body problem
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Continuation of periodic orbits in conservative and Hamiltonian systems
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Interval Methods for Systems of Equations
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A note on the existence of invariant punctured tori in the planar circular restricted three-body problem
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Verification methods: Rigorous results using floating-point arithmetic
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Periodic and Chaotic Trajectories of the Second Species for the n-Centre Problem
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Global Bifurcations of Periodic solutions of the Hill Lunar Problem*
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Successive continuation for locating connecting orbits
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Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem
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ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
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A family of retrograde orbits around the triangular equilibrium points
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Consecutive quasi-collisions in the planar circular RTBP
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The existence of simple choreographies for theN-body problem—a computer-assisted proof
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Connecting orbits and invariant manifolds in the spatial restricted three-body problem
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On the construction of the Kolmogorov normal form for the Trojan asteroids
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Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight
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Numerical continuation of families of homoclinic connections of periodic orbits in the RTBP
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Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system
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Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
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Torus knot choreographies in the n -body problem
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Rigorous Numerics in Dynamics
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Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits
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Improbability of Collisions in Newtonian Gravitational Systems
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Improbability of Collisions in Newtonian Gravitational Systems. II
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Triple collisions in the isosceles 3-body problem
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The Numerical Computation of Connecting Orbits in Dynamical Systems
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Stability and Multiplicity of Solutions to Discretizations of Nonlinear Ordinary Differential Equations
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Existence of a Center Manifold in a Practical Domain around $L_1$ in the Restricted Three-Body Problem
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Computer Assisted Existence Proofs of Lyapunov Orbits at $L_2$ and Transversal Intersections of Invariant Manifolds in the Jupiter--Sun PCR3BP
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Stationary Coexistence of Hexagons and Rolls via Rigorous Computations
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Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method
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Computer-Assisted Proofs in Analysis and Programming in Logic: A case Study
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Dynamics and Mission Design Near Libration Points
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Dynamics and Mission Design Near Libration Points
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N-BODY CHOREOGRAPHIES WITH A REFLECTIONAL SYMMETRY - COMPUTER ASSISTED EXISTENCE PROOFS
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SHADOWING CHAINS OF COLLISION ORBITS FOR THE ELLIPTIC 3-BODY PROBLEM
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Numerical continuation of periodic orbits in symmetric hamiltonian systems
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Dynamical Systems, the Three-Body Problem and Space Mission Design
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Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem
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TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS
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CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (I): POINT-TO-CYCLE CONNECTIONS
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CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (II) : CYCLE-TO-CYCLE CONNECTIONS
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Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
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Computer Assisted Proof of Homoclinic Chaos in the Spatial Equilateral Restricted Four Body Problem
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Symmetric regularization, reduction and blow-up of the planar three-body problem
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Sur l'allure du mouvement dans le problème des trois corps quand le temps croît indéfiniment
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Branches of periodic orbits for the planar restricted 3-body problem
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Computer-assisted estimates for Birkhoff normal forms
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Arnold Diffusion, Quantitative Estimates and Stochastic Behavior in the Three-Body Problem
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Celestial mechanics: the waltz of the planets
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