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Symmetry of planar four-body convex central configurations
We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with
Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter
Four-Body Central Configurations¶with some Equal Masses
Abstract We prove firstly that any convex non-collinear central configuration of the planar 4-body problem with equal opposite masses β >α > 0, such that the diagonal corresponding to the mass α is
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
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
The non-existence of bi-Lipschitz embedding of sub-Riemannian manifold in Banach spaces with Radon-Nikodym property
In this paper, we prove that there do not exist quasi-isometric embeddings of connected, simply connected non-abelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a
Collinear Central Configurations and Singular Surfaces in the Mass Space
Abstract.For a given m=(m1,...,mn)∈(R+)n, let p and q∈(R3)n be two central configurations for m. Then we call p and qequivalent and write p∼q if they differ by an SO(3) rotation followed by a scalar
Morse index and the stability of closed geodesics
AbstractLet ind(c) be the Morse index of a closed geodesic c in an (n+1)-dimensional Riemannian manifold $$ \mathcal{M} $$. We prove that an oriented closed geodesic c is unstable if n + ind(c) is