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math.DS2026
Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric -Body Problems
Hangqi Liang, Zhihong Xia, Tingjie Zhou
Many mechanical systems, such as the Newtonian -body system, are invariant under rotations. The rotational symmetry of the system gives rise to two commuting actions: the dynami…
math.DS2026
On the Degeneracy of the Central Configuration Formed by a Regular n-Gon with a Central Mass
Tingjie Zhou, Zhihong Xia
We investigate the degeneracy of the central configuration formed by a regular -gon of equal masses together with an additional mass at the center. While degeneracy of such conf…
math.DS2024
Central Configurations with Dihedral Symmetry
Tingjie Zhou, Zhihong Xia
As an application of the representation theory for the dihedral groups, we study the symmetric central configurations in the n-body problem where equal masses are placed at the…