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arXiv · 2603.06277

On the Combinatorial Rigidity for Polynomials with Attracting Cycles

Yueyang Wang
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Abstract

We show that every polynomial of degree $d \geq 2$ in the connectedness locus with an attracting cycle which attracts at least two critical points and no indifferent cycles is not combinatorially rigid. In particular, we prove that a hyperbolic polynomial with connected Julia set is combinatorially rigid if and only if it is of the ``disjoint type''.

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Yueyang Wang. 2026-03-06. On the Combinatorial Rigidity for Polynomials with Attracting Cycles. https://arxiv.org/abs/2603.06277

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