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Structurally unstable quadratic vector fields of codimension-two: families possessing one infinite saddle-node of type (0,2) and a separatrix connection

Joan C. Artés

This paper is part of a series of works whose ultimate goal is the complete classification of phase portraits of quadratic differential systems in the plane modulo limit cycles. Time ago, it was estimated that the total number could be around 2000, but the recent compilation of the Quadripedia ``http://gsd.uab.cat/Quadripedia'' (an electronic database of all known quadratic systems up to now) gives a number over 1150 cases and it seems to be quite closer to the final number. Anyway the work to find them all must be split in different papers in a systematic way so to assure the completeness of the study and also the non intersection among them. In this paper we classify the family of phase portraits possessing one infinite saddle-node with first eigenvalue of the Jacobian matrix equal to 0, plus a separatrix connection and determine that there are a minimum of 49 topologically different phase portraits plus at most 16 other phase portraits which we conjecture to be impossible.

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