Abstract by Mitchell Sailsbery
Numerical Evidence for Non-integrability of the Two-Center Symmetric Pair Problem for Negative Energy
The two center symmetric pair problem can be seen as a perturbation of Euler’s two center problem. Before perturbation, the problem is globally Liouville integrable. We present evidence that after the perturbation, the integrability ceases to be global. This result is already known for positive energy but here we show that this evidence also suggests non-integrability for the negative energy case. Then, future research ideas are discussed.