23 citations · 47 across the 17 of their papers we have counts for
20 papers
Approach to total collision in the spatial 4-body problem
Richard Montgomery, Guowei Yu
Every solution for the classical four body problem in space which ends in total collision has a limiting shape. We prove that when that shape is planar the entire solution lies in…
Integrable variant Blaszak-Szum lattice equation
Wei-Kang Xie, Guo-Fu Yu
We derive a novel variant of the Blaszak-Szum lattice equation by introducing a new class of trigonometric-type bilinear operators. By employing Hirota's bilinear method, we obtain…
Variational Construction of Homoclinic and Heteroclinic Orbits in the Planar Sitnikov Problem
Yuika Kajihara, Mitsuru Shibayama, Guowei Yu
The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions i…
The problem of infinite Spin for parabolic and collision solutions in the planar -body problem
Zhe Wang, Guowei Yu
In the planar -body problem, the problem of infinite spin occurs for both parabolic and collision solutions. Recently Moeckel and Montgomery \cite{MM25} showed that there is no…
Relative periodic solutions in spatial Kepler problem with symmetric perturbation
Xijun Hu, Zhiwen Qiao, Guowei Yu
The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the -axis and the reflection symmetry w.r.t. the -plane, can be reduced to an Ha…
Positive energy solutions in the anisotropic Kepler problem with homogeneous potential
Guowei Yu
We study positive energy solutions of the anisotropic Kepler problem with homogeneous potential. First some asymptotic property of positive energy solutions is obtained, as time go…
Hyperbolic motions in the -body problem with homogeneous potentials
Guowei Yu
In the -body problem, a motion is called hyperbolic, when the mutual distances between the bodies go to infinity with non-zero limiting velocities as time goes to infinity. For…
A symplectic dynamics approach to the spatial isosceles three-body problem
Xijun Hu, Lei Liu, Yuwei Ou +2
We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the…
Hyperbolic and Bi-hyperbolic solutions in the planar restricted -body problem
Guowei Yu
Consider the planar restricted -body problem with trajectories of the primaries forming a collision-free periodic solution of the -body problem, for any positi…
Regularizable collinear periodic solutions in the -body problem with arbitrary masses
Guowei Yu
For -body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary…
Global Surfaces of Section and Periodic Orbits in The Spatial Isosceles Three Body Problem
Xijun Hu, Lei Liu, Yuwei Ou +1
We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momen…
Chazy-Type Asymptotics and Hyperbolic Scattering for the -Body Problem
Nathan Duignan, Richard Moeckel, Richard Montgomery +1
We study solutions of the Newtonian -body problem which tend to infinity hyperbolically, that is, all mutual distances tend to infinity with nonzero speed as $t \rightarrow +\in…
An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian -body Problem
Xijun Hu, Yuwei Ou, Guowei Yu
In the Newtonian -body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic resul…
Application of Morse index in weak force -body problem
Guowei Yu
Due to collision singularities, the Lagrange action functional of the N-body problem in general is not differentiable. Because of this, the usual critical point theory can not be a…
Connecting planar linear chains in the spatial -body problem
Guowei Yu
The family of planar linear chains are found as collision-free action minimizers of the spatial -body problem with equal masses under or $D_N \times \zz_2$-symmetry constr…
Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem
Xijun Hu, Guowei Yu
In the variational study of singular Lagrange systems, the zero energy solutions play an important role. In this paper we find a simple way of computing the Morse indices of these…
Spatial double choreographies of the Newtonian -body problem
Guowei Yu
In this paper, for the spatial Newtonian -body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone c…
Simple choreographies of the planar Newtonian -body Problem
Guowei Yu
In the -body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian -…
Shape Space Figure- Solution of Three Body Problem with Two Equal Masses
Guowei Yu
In a preprint by Montgomery \cite{Mo99}, the author attempted to prove the existence of a shape space Figure- solution of the Newtonian three body problem with two equal masses…
Periodic Solutions of the Planar N-Center Problem with topological constraints
Guowei Yu
In the planar -center problem, for a non-trivial free homotopy class of the configuration space satisfying certain mild condition, we show that there is at least one collision f…