3 citations · 11 across the 14 of their papers we have counts for
14 papers
Symbolic Computations of the Two-Colored Diagrams for Central Configurations of the Planar N-vortex Problem
Xiang Yu, Shuqiang Zhu
We apply the singular sequence method to investigate the finiteness problem for stationary configurations of the planar N-vortex problem. The initial step of the singular sequence…
Two Colored Diagrams for Central Configurations of the Planar Five-vortex Problem
Xiang Yu, Shuqiang Zhu
We apply the singular sequence method to investigate the finiteness problem for stationary configurations of the planar five-vortex problem. The initial step of the singular sequen…
The Schubart orbits on the circle
Shuqiang Zhu
We consider the three body problem on under the cotangent potential. We first construct homothetic orbits ending in singularities, including total collision singularity and c…
Odd index of the amended potential implies linear instability
Yanxia Deng, Shuqiang Zhu
For a relative equilibrium of a symmetric simple mechanical system, if the Morse index of the corresponding amended potential is odd, whether the nullity is zero or not, it is line…
On Finiteness of Stationary Configurations of the Planar Five-vortex Problem
Xiang Yu, Shuqiang Zhu
The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations…
On the finiteness of four-body central configurations
Xiang Yu, Shuqiang Zhu
The number of central configurations in the four body problem was proved to be finite, first by Hampton and Moeckel, then by Albouy and Kaloshin, when the masses are all positive.…
Compactness and index of ordinary central configurations for the curved n-body problem
Shuqiang Zhu
For the curved n-body problem, we show that the set of ordinary central configurations is away from most singular configurations in H^3, and away from a subset of singular configur…
Regular polygonal equilibrium configurations on S^1 and stability of the associated relative equilibria
Xiang Yu, Shuqiang Zhu
For the curved n-body problem in S^3, we show that a regular polygonal configuration for n masses on a geodesic is an equilibrium configuration if and only if n is odd and the mass…
Classification of stacked central configurations in R^3
Xiang Yu, Shuqiang Zhu
We classify the extensions of n-body central configurations to (n + 1)-body central configurations in R3, in both the collinear case and the non-collinear case. We completely solve…
Dziobek equilibrium configurations on a sphere
Shuqiang Zhu
We investigate the n-body problem on a sphere with a general interaction potential that depends on the mutual distances. We focus on the equilibrium configurations, especially on t…
A Lower Bound for the Number of Central Configurations on H^2
Shuqiang Zhu
We study the indices of the geodesic central configurations on $\H^2$. We then show that central configurations are bounded away from the singularity set. With Morse's inequality,…
The -Body Problem in Spaces with Uniformly Varying Curvature
Eric Boulter, Florin Diacu, Shuqiang Zhu
We generalize the curved -body problem to spheres and hyperbolic spheres whose curvature varies in time. Unlike in the particular case when the curvature is constant, the eq…
Three dimensional central configurations in H3 and S3
Suo Zhao, Shuqiang Zhu
We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. Ho…
Stability of fixed points and associated relative equilibria of the -body problem on and
Florin Diacu, Juan Manuel Sánchez-Cerritos, Shuqiang Zhu
We prove that the fixed points of the curved 3-body problem and their associated relative equilibria are Lyapunov stable if the solutions are restricted to , but unsta…