Versal normal form of the Hamiltonian function of the restricted problem of three bodies near \({\mathcal L}_ 4\)

DOI10.1016/0377-0427(94)90355-7zbMath0815.58021OpenAlexW2044040807MaRDI QIDQ1342924

Dieter S. Schmidt

Publication date: 11 July 1995

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90355-7

zbMATH Keywords

periodic solutionsproblem of three bodiesversal normal form

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (13)

The evolution of invariant manifolds in Hamiltonian-Hopf bifurcations ⋮ Hopf bifurcation for the hydrogen atom in a circularly polarized microwave field ⋮ Miniversal deformations of matrices under *congruence and reducing transformations ⋮ Stability of equilibrium solutions of Hamiltonian systems under the presence of a single resonance in the non-diagonalizable case ⋮ Reeb's theorem and periodic orbits for a rotating Hénon-Heiles potential ⋮ Unnamed Item ⋮ Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points ⋮ From the restricted to the full three–body problem ⋮ Transformation to versal deformations of matrices ⋮ On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance ⋮ A study of the motions of an autonomous Hamiltonian system at a 1:1 resonance ⋮ On Nonlinear Oscillations of a Near-Autonomous Hamiltonian System in the Case of Two Identical Integer or Half-Integer Frequencies ⋮ Normal forms for Hamiltonian systems in some nilpotent cases

Cites Work

• A simple global characterization for normal forms of singular vector fields
• Normal forms and versal deformations of linear Hamiltonian systems
• Versal normal form at the Lagrange equilibrium \(L_ 4\)
• Versal deformations of linear Hamiltonian systems
• Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues
• Canonical transformations depending on a small parameter
• Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh
• ON MATRICES DEPENDING ON PARAMETERS
• Unnamed Item
• Unnamed Item
• Unnamed Item

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