On Poincaré’s Fourth and Fifth Examples of Limit Cycles at Infinity
نویسنده
چکیده
Errors are found in example problems from Henri Poincaré’s paper “Mémoire sur les courbes définies par une équation différentielle.” Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poincaré, examples four and five are studied at length. Replacement equations for the fourth and fifth examples are suggested based on the supposition that terms were omitted from Poincaré’s equations.
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