The existence of a Smale horseshoe in a planar circular restricted four-body problem

DOI10.1007/s10569-013-9528-1zbMath1293.70049OpenAlexW2004441360MaRDI QIDQ399977

Zhikun She, Xuhua Cheng

Publication date: 20 August 2014

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

Full work available at URL: https://doi.org/10.1007/s10569-013-9528-1

zbMATH Keywords

chaotic dynamicsPoincaré mapSmale horseshoeConley-Moser conditionsSmale-Birkhoff theorem

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) (n)-body problems (70F10) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44)

Related Items (10)

A note on the existence of a Smale horseshoe in the planar circular restricted three-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 ⋮ Unnamed Item ⋮ 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 ⋮ 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 ⋮ Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

Cites Work

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