58 citations · 67 across the 15 of their papers we have counts for
4 papers · 1 filter
On the Uniqueness of Convex Central Configurations in the Planar -Body Problem
Shanzhong Sun, Zhifu Xie, Peng You
In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that there exists a unique convex central configuration for any four fixed positive masses in a…
Elliptic fixed points with an invariant foliation: Some facts and more questions
Alain Chenciner, David Sauzin, Shanzhong Sun +1
We address the following question: let F:(R^2,0)->(R^2,0) be an analytic local diffeomorphism defined in the neighborhood of the non resonant elliptic fixed point 0 and let Φbe a f…
Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic Paths
Shanzhong Sun
Gutzwiller's famous semiclassical trace formula plays an important role in theoretical and experimental quantum mechanics with tremendous success. We review the physical derivation…
Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
Xijun Hu, Yiming Long, Shanzhong Sun
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 paramete…