## 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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