On the ``blue sky catastrophe termination in the restricted four-body problem

DOI10.1007/s10569-013-9498-3zbMath1293.70050arXiv1210.0144OpenAlexW2034476542MaRDI QIDQ399964

Jaime Burgos-García, Joaquín Delgado

Publication date: 20 August 2014

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0144

zbMATH Keywords

stabilityperiodic orbitsequilibrium pointsnormal form theorytransverse intersections

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (14)

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration ⋮ Hill's approximation in a restricted four-body problem ⋮ Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four-body problem ⋮ Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem ⋮ A family of models with blue sky catastrophes of different classes ⋮ Analytical study on the motions around equilibrium points of restricted four-body problem ⋮ Homoclinic dynamics in a spatial restricted four-body problem: blue skies into Smale horseshoes for vertical Lyapunov families ⋮ Study on Chaotic Behavior of the Restricted Four-Body Problem with an Equilateral Triangle Configuration ⋮ Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set ⋮ Hill four-body problem with oblate bodies: an application to the Sun-Jupiter-Hektor-Skamandrios system ⋮ Critical homoclinics in a restricted four-body problem: numerical continuation and center manifold computations ⋮ Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem ⋮ The spatial Hill four-body problem. I: An exploration of basic invariant sets ⋮ A note on the relative equilibria bifurcations in the \((2N+1)\)-body problem

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