ON POINCARÉ'S FOURTH
AND FIFTH EXAMPLES OF
LIMIT CYCLES AT INFINITY

ROLAND K.W. ROEDER

Abstract:

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.