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arXiv · 2601.18605

Polynomials in molecules

Yan Gao·Jinsong Zeng
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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.

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Yan Gao, Jinsong Zeng. 2026-01-26. Polynomials in molecules. https://arxiv.org/abs/2601.18605

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