Goodness of generic two-parameter families on the two-sphere

A family of vector fields on the two-sphere is called good when it is moderately structurally stable. A two-parameter family has a two-dimensional parameter space, and generic means belonging to the relevant generic class.

Good-family conjecture for two parameters. Generic two-parameter families of vector fields in the two-sphere are good.

This is part of the paper's good, bad and ugly classification of finite-parameter families. The supplied context gives no resolution and the later discussion treats classification of generic two-parameter families as far from solved.