Rigidity of Lyapunov exponents for polynomials
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908905662054400 |
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| author | Ji, Zhuchao Xie, Junyi Zhang, Geng-Rui |
| author_facet | Ji, Zhuchao Xie, Junyi Zhang, Geng-Rui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity of Lyapunov exponents for polynomials Ji, Zhuchao Xie, Junyi Zhang, Geng-Rui Dynamical Systems Algebraic Geometry Number Theory Primary 37P05, Secondary 37P15, 37P30 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. |
| title | Rigidity of Lyapunov exponents for polynomials |
| topic | Dynamical Systems Algebraic Geometry Number Theory Primary 37P05, Secondary 37P15, 37P30 |
| url | https://arxiv.org/abs/2603.21179 |