Coexistence of critical orbit types in sub-hyperbolic polynomial maps
Dynamical Systems
2008-02-03 v1
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.
Cite
@article{arxiv.math/9406230,
title = {Coexistence of critical orbit types in sub-hyperbolic polynomial maps},
author = {Alfredo Poirier},
journal= {arXiv preprint arXiv:math/9406230},
year = {2008}
}