3 papers
math.DS2025
Degeneracy of Planar Central Configurations in the -Body Problem
Shanzhong Sun, Zhifu Xie, Peng You
The degeneracy of central configurations in the planar -body problem makes their enumeration problem hard and the related dynamics appealing. To truly understand the bifurcation…
math.DS2023
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…
math-ph2022
Monodromy of Complexified Planar Kepler Problem
Shanzhong Sun, Peng You
The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.