ABSTRACT
This chapter shows that the results of the last chapter continue to hold when one allow for higher order terms and more complicated dependence on ?. It shows that provided we exclude a ‘thin’ set of homogeneous cubic polynomials, the results of the last chapter hold when we allow for higher order terms. Methods will make use of generalized polar coordinates or, what one usually call, (polar) blowing-up. This type of coordinate transformation is very geometric and has the advantage of exhibiting the underlying structure in a transparent way. More importantly for us, the use of polar blowing-up will form an essential part of toolkit when one start investigating the dynamics that are spawned at bifurcation points.
