Quadratic and Cubic Systems with Degenerate Infinity

We obtain an affine classification of quadratic systems with degenerate infinity in eight types and prove that they present 13 phase portraits on the Poincare´ sphere. For cubic systems with degenerate infinity the situation is much more complicated. We show that there are examples of such systems with at least three concentric limit cycles and we give a criterion to ensure that, in some cases, this number is less than or equal to two.