Hyperbolicity of elliptic Lagrangian orbits in the planar three body problem

DOI10.1007/s11425-014-4784-4zbMath1299.70021OpenAlexW2254407509MaRDI QIDQ477127

Yuwei Ou

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-014-4784-4

zbMATH Keywords

hyperbolicityMaslov-type indexLagrangian solutionplanar three-body problem

Mathematics Subject Classification ID

Three-body problems (70F07) Hamilton's equations (70H05) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (5)

Linear stability of elliptic relative equilibria of restricted four-body problem ⋮ Trace estimation of a family of periodic Sturm-Liouville operators with application to Robe’s restricted three-body problem ⋮ An estimation for the hyperbolic region of elliptic Lagrangian solutions in the planar three-body problem ⋮ Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions ⋮ Collision index and stability of elliptic relative equilibria in planar \(n\)-body problem

Cites Work

• Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
• Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit
• Bott formula of the Maslov-type index theory
• Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem
• Index theory for symplectic paths with applications
• Stability diagram for 4D linear periodic systems with applications to homographic solutions
• Analysis of the stability of a family of singular-limit linear periodic systems in \(\mathbb {R}^4\). Applications
• STABILITY OF HOMOGRAPHIC SOLUTIONS OF THE PLANAR THREE-BODY PROBLEM WITH HOMOGENEOUS POTENTIALS

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