Chaotic dynamics near triple collision

DOI10.1007/BF00251426zbMath0697.70021OpenAlexW2044509176MaRDI QIDQ911822

Richard Moeckel

Publication date: 1989

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251426

zbMATH Keywords

periodic orbitsthree-body problemsymbolic dynamicsheteroclinic connectionsunstable manifoldsEulerian orbitsLagrangian orbitsLagrangian restpoints

Mathematics Subject Classification ID

Three-body problems (70F07) Bifurcations and instability for nonlinear problems in mechanics (70K50) Collision of rigid or pseudo-rigid bodies (70F35)

Related Items (23)

Secular instability in the three-body problem ⋮ Free time minimizers for the three-body problem ⋮ Spiralling invariant manifolds ⋮ Entire parabolic trajectories as minimal phase transitions ⋮ An index theory for zero energy solutions of the planar anisotropic Kepler problem ⋮ An index theory for collision, parabolic and hyperbolic solutions of the Newtonian \(n\)-body problem ⋮ Geometric properties of minimizers in the planar three-body problem with two equal masses ⋮ The rectilinear three-body problem using symbol sequence. I: Role of triple collision ⋮ Asymptotic density of collision orbits in the restricted circular planar 3 body problem ⋮ Triple collision orbits with nonzero initial velocities ⋮ Breakdown of homoclinic orbits to \(L_3\) in the RPC3BP. II: An asymptotic formula ⋮ Symbolic dynamics in the planar three-body problem ⋮ Ejection-collision orbits in two degrees of freedom problems in celestial mechanics ⋮ Collective branch regularization of simultaneous binary collisions in the 3D N-body problem ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ Exponential stability of fast driven systems, with an application to celestial mechanics ⋮ The zero angular momentum, three-body problem: All but one solution has syzygies ⋮ Analysis of the stability of a family of singular-limit linear periodic systems in \(\mathbb {R}^4\). Applications ⋮ Collision index and stability of elliptic relative equilibria in planar \(n\)-body problem ⋮ Finiteness of stationary configurations of the four-vortex problem ⋮ The flow of the \(N\)-body problem near a simultaneous-binary-collision singularity and integrals of motion on the collision manifold ⋮ Numerical confirmation of the existence of triple collision orbits inside the domain of the free-fall three-body problem ⋮ Equilateral chains and cyclic central configurations of the planar five-body problem

Cites Work

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• Topology and mechanics. I
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• Heteroclinic Phenomena in the Isosceles Three-Body Problem
• Orbits of the Three-Body Problem Which Pass Infinitely Close to Triple Collision
• The three-body problem near triple collision
• Structural stability of homothetic solutions of the collinearn-body problem

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