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Coexistence of critical orbit types in sub-hyperbolic polynomial maps

Alfredo Poirier
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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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Alfredo Poirier. 1994-06-17. Coexistence of critical orbit types in sub-hyperbolic polynomial maps. https://arxiv.org/abs/math/9406230

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