| Abstract: |
| Enumeration problems for the central configurations of the Newtonian $n$ body problem are hard for $n>3$ in $\mathbb{R}^{2}$ and $n>4$ in $\mathbb{R}^{3}$. These are problems in finding the numbers of classes of the central configurations for all the masses in a parameter space of positive dimensions. Many results are obtained generically. That is, rigorous proofs of the counting problems only exists for parameters not at the bifurcation points. For the bifurcation points, only numerical evidences are provided due to the complexity of the problems.
In this talk, I will propose an algorithm that rigorously proves results on counting central configurations for all masses in one dimensional parameter spaces. Some examples on central configuration problems solved by our method will be presented. |
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