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Symmetry of planar four-body convex central configurations

- A. Albouy, Yanning Fu, Shanzhong Sun
- MathematicsProceedings of the Royal Society A: Mathematical…
- 8 June 2007

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… Expand

Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory

- Xijun Hu, Y. Long, Shanzhong Sun
- Mathematics
- 27 June 2012

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… Expand

Four-Body Central Configurations¶with some Equal Masses

- Y. Long, Shanzhong Sun
- Mathematics
- 1 March 2002

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… Expand

Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit

- Xijun Hu, Shanzhong Sun
- Mathematics
- 7 July 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… Expand

Stability of relative equilibria and Morse index of central configurations

- Xijun Hu, Shanzhong Sun
- Mathematics
- 1 November 2009

The non-existence of bi-Lipschitz embedding of sub-Riemannian manifold in Banach spaces with Radon-Nikodym property

- Yonghong Huang, Shanzhong Sun
- Mathematics
- 17 January 2018

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… Expand

Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem

- Xijun Hu, Shanzhong Sun
- Mathematics
- 15 January 2010

Collinear Central Configurations and Singular Surfaces in the Mass Space

- Y. Long, Shanzhong Sun
- Mathematics
- 31 March 2004

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… Expand

Morse index and the stability of closed geodesics

- Xijun Hu, Shanzhong Sun
- Mathematics
- 24 April 2010

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… Expand

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