Institute for Mathematical Sciences

Preprint ims94-10

A. Poirier
Coexistence of Critical Orbit Types in Sub-Hyperbolic Polynomial Maps

Abstract: We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\bf C} to itself which have degree two or more in each copy. As a consequence of these results we prove a transitivity relation between hyperbolic components in parameter space which was conjectured by Milnor.
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