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On the Stability of Lagrange Relative Equilibrium in The Planar Three-body Problem
Xiang Yu
Since the strong degeneracies present in the N-body problem, even in the basic case of the planar three-body problem, nobody inspects the problem of nonlinear stability of Lagrange…
On the Problem of Infinite Spin in Total Collisions of the Planar N-Body Problem
Xiang Yu
For the planar -body problem, we first introduce a class of moving frame suitable for orbits near central configurations, especially for total collision orbits, which is the mai…
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…
New homoclinic orbits for Hamiltonian systems with asymptotically quadratic growth at infinity
Dong-Lun Wu, Xiang Yu
In this paper, we study the existence and multiplicity of homoclinic solutions for following Hamiltonian systems with asymptotically quadratic nonlinearities at infinity \begin{eqn…