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The best applications of the Poincaré-Bendixson theorem [closed]

I'm reading about the Poincaré-Bendixson theorem in the plane, I really liked the theorem. I have seen common applications in Sotomayor and Perko's book. But I would like to know what other ...
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Can iterative application of ham sandwich cuts form streamlines of an ODE?

It has been known that given two probability distributions $\mu_1$ and $\mu_2$ (let us say, they are smooth for simplicity), there is a hyperplane that divides the domain into two regions (denoted as $...
user483904's user avatar