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arXiv · 2603.21179

Rigidity of Lyapunov exponents for polynomials

Zhuchao Ji·Junyi Xie·Geng-Rui Zhang
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Abstract

Let $f,g\in\overline{\mathbb{Q}}[z]$ be polynomials of degree $d\geq2$ with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g$ if and only if either $f$ and $g$ are intertwined, or $f$ and $\overline{g}$ are intertwined. The analogous result for critical heights is also obtained. As an application, we provide a new proof of the theorem stating that the multiplier spectrum morphism on the moduli space of polynomials is generically injective.

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Zhuchao Ji, Junyi Xie, Geng-Rui Zhang. 2026-03-22. Rigidity of Lyapunov exponents for polynomials. https://arxiv.org/abs/2603.21179

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