8 Hole-cutting as an active component of the folding process

The "hole-cutting'' technique was introduced in Roscoe 1999A on the basis of the qualitative argument that the interior parts of rotation curves must be significantly disturbed by the presence of the bulge. This argument is given quantitative support in Appendix B, where it is explicitly shown how hole-cutting has a very powerful effect on the quality of the power-law fits to rotation curves; furthermore, it is shown in Appendix C, how the cut-out sections can be interpreted as dynamical transition regions on the interiors of rotation curves.

So far, however, the hole-cutting process has played no active part in the actual folding process - that is, we have so far assumed that rotation curves should be folded using all of the available data. This latter assumption is justified if the transition regions are as asymmetric about the dynamical centres as the exterior parts of rotation curves are assumed to be.

But, by the very nature of "dynamical transition regions'' in the generality of physical systems, the possibility exists that the dynamics in such regions is, to some extent, chaotic. In this latter case, the shapes of the interior parts of rotation curves could be then significantly disturbed from the asymmetry assumed for the exterior parts of rotation curves - and this would lead to systematic inaccuracies in the final solutions due entirely to the inclusion of the transition regions in the folding process. It would then follow that using only the exterior parts of rotation curves for the folding process will lead to more accurate folding.