| Abstract: |
| Central configurations play crucial roles in comprehending the solution structure and dynamic behavior of the N-body problem. The renowned Chazy-Wintner-Smale conjecture states that, for any given positive masses, there exists only a finite number of central configurations. While the conjecture has been verified for the planar 4-body problem and partially for the planar 5-body problem, its generalization remains a formidable challenge for 21st-century mathematicians. The precise enumeration of central configurations for the 4-body problem remains an ongoing pursuit. Particularly the classifications of planar 4-body central configurations have attracted numerous researchers exploring various notions of symmetry within configuration and mass spaces. In this presentation, we will review the findings regarding central configurations for the four-body problem, as well as our recent contributions to this field. |
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