Other Approaches

Abstract

In this final chapter I want to mention briefly three other approaches to the general center-focus problem. In the first, we try to identify whole components of the center variety by finding their intersections with specific subsets of parameter space and then showing that the type of center is “rigid”. In the second approach, we try to see the consequences of a center on its bounding graphic. Monodromytype arguments play an implicit role in both of these approaches. The last section describes an experimental approach to the center-focus via intensive computations using modular arithmetic and an application of the Weil conjectures. It makes a fitting conclusion to our range of monodromy techniques, since the arithmetic analog of monodromy was an essential ingredient in Deligne’s proof of the Weil conjectures [27].