Linear instability of elliptic rhombus solutions to the planar four-body problem
DOI10.1088/1361-6544/ac288ezbMath1476.58013arXiv1806.01641OpenAlexW3207686385MaRDI QIDQ5160607
Publication date: 29 October 2021
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.01641
linear stabilityMorse indexhyperbolic regionplanar four-body problem\(\omega\)-Maslov indexelliptic rhombus solution
Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)
Cites Work
- Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
- Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
- Bott formula of the Maslov-type index theory
- Finiteness and bifurcations of some symmetrical classes of central configurations
- Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
- Four-body central configurations with some equal masses
- Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem
- Instability for a family of homographic periodic solutions in the parallelogram four body problem
- Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem
- Perturbation theory for linear operators.
- On central configurations
- Index theory for symplectic paths with applications
- Linear stability of elliptic relative equilibria of restricted four-body problem
- Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions
- The reduction of the linear stability of elliptic Euler-Moulton solutions of the \(n\)-body problem to those of 3-body problems
- Structure and stability of the rhombus family of relative equilibria under general homogeneous forces
- An estimation for the hyperbolic region of elliptic Lagrangian solutions in the planar three-body problem
- Elliptic relative equilibria in the \(N\)-body problem
- Stability diagram for 4D linear periodic systems with applications to homographic solutions
- Convex four-body central configurations with some equal masses
- Symmetry of planar four-body convex central configurations
- Admissible Shapes of 4-Body Non-collinear Relative Equilibria
- Linear stability of the elliptic relative equilibrium with (1 + n)-gon central configurations in planar n-body problem
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