Coexistence of critical orbit types in sub-hyperbolic polynomial maps

1994/06/17 by Poirier, Alfredo
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9406230

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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• Hyperbolic Components
• Hyperbolic components of polynomials with a fixed critical point of maximal order
• Special curves and postcritically-finite polynomials
• Cubic Polynomial Maps with Periodic Critical Orbit, Part III: Tessellations and Orbit Portraits