## Chicone Dinner Problem

A prize to consist of dinner for two at the restaurant of your choice in Columbia Missouri (transportation to Columbia not included) is offered for the first valid solution of the following problem:

Let H denote the space of homogeneous cubic polynomials in three variables and let A denote the subset of H consisting of those elements whose gradients (orthogonally) project to a vector field on the unit sphere such that the corresponding dynamical system has no saddle connections. Prove or disprove that A is a dense subset of H in the coefficient topology (see Exercise 1.73 in Ordinary Differential Equations with Applications).

A submitted proof must be complete and clear. At least, I must be able to understand it! Decisions by me will be final.