Polynomials in molecules

Abstract

This paper characterizes polynomials within molecules. We show that a geometrically finite polynomial of degree $d\ge 2$ 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.

30 pages, 2 figures