Branches of periodic orbits for the planar restricted 3-body problem

DOI10.3934/dcds.2004.11.745zbMath1060.37070OpenAlexW2080518444MaRDI QIDQ1766137

Gianni Arioli

Publication date: 28 February 2005

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2004.11.745

zbMATH Keywords

stabilityexistencebranches of periodic solutionsplanar restricted 3-body problem

Mathematics Subject Classification ID

Three-body problems (70F07) Stability for nonlinear problems in mechanics (70K20) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems in classical and celestial mechanics (37N05) Stability theory for smooth dynamical systems (37C75)

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Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem ⋮ Automatic differentiation for Fourier series and the radii polynomial approach ⋮ Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence ⋮ Systematic computer assisted proofs of periodic orbits of Hamiltonian systems ⋮ Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

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