Polynomials in molecules
Abstract
This paper characterizes polynomials within molecules. We show that a geometrically finite polynomial of degree $d\geq2$ 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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Holomorphic and Operator Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 January 2026
- Document type
- Preprint