| Abstract: |
| The system of central configuration equations includes invariants such as scaling, rotation, and translation, which introduce trivial zero eigenvalues to the Jacobian matrix for a central configuration. To determine if a central configuration undergoes a bifurcation, it is crucial to identify if there is a non-trivial zero eigenvalue. In this talk, we will discuss methods to isolate these trivial zero eigenvalues, allowing us to compute the determinant of the remaining matrix. If this determinant is non-zero, it indicates that no bifurcation occurs. |
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