Polynomials in molecules
Abstract
This paper characterizes polynomials within molecules. We show that a geometrically finite polynomial of degree d≥2 lies in a molecule if and only if all its critical points belong to maximal Fatou chains, and show that distinct molecules are mutually disjoint. We also establish a necessary and sufficient condition for subhyperbolic polynomials to be on the closures of bounded hyperbolic components.
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