Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
@article{Hu2010MorseIA, title={Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem}, author={Xijun Hu and Shanzhong Sun}, journal={Advances in Mathematics}, year={2010}, volume={223}, pages={98-119} }
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References
SHOWING 1-10 OF 38 REFERENCES
Linear Stability of the Elliptic Lagrangian Triangle Solutions in the Three-Body Problem
- Physics, Mathematics
- 2002
Abstract This paper concerns the linear stability of the well-known periodic orbits of Lagrange in the three-body problem. Given any three masses, there exists a family of periodic solutions for…
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
- Mathematics
- 2009
In this paper, using the Maslov index theory in symplectic geometry, we build up some stability criteria for symmetric periodic orbits in a Hamiltonian system, which is motivated by the recent…
Linear stability analysis of the figure-eight orbit in the three-body problem
- MathematicsErgodic Theory and Dynamical Systems
- 2007
Abstract We show that the well-known figure-eight orbit of the three-body problem is linearly stable. Building on the strong amount of symmetry present, the monodromy matrix for the figure-eight is…
Iteration Inequalities of the Maslov-Type Index Theory with Applications
- Mathematics
- 2000
Abstract In this paper, by using the ω-index theory introduced by Y. Long in (1999, Pacific J. Math.187, 113–149), in particular, the splitting numbers, Maslov-type mean index, and the homotopy…
Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
- Mathematics
- 1984
An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic…
MASLOV-TYPE INDEX, DEGENERATE CRITICAL POINTS, AND ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
- Mathematics
- 1990
This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of…
The N-body problem, the braid group, and action-minimizing periodic solutions
- Mathematics
- 1998
A reduced periodic orbit is one which is periodic modulo a rigid motion. If such an orbit for the planar N-body problem is collision free then it represents a conjugacy class in the projective…
A remarkable periodic solution of the three-body problem in the case of equal masses
- Physics, Geology
- 2000
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry…
On the existence of collisionless equivariant minimizers for the classical n-body problem
- Mathematics, Physics
- 2004
We show that the minimization of the Lagrangian action functional on suitable classes of symmetric loops yields collisionless periodic orbits of the n-body problem, provided that some simple…