The multiplier spectrum morphism is generically injective
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914049900412928 |
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| author | Ji, Zhuchao Xie, Junyi |
| author_facet | Ji, Zhuchao Xie, Junyi |
| contents | In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexible Lattès family, the multiplier spectrum morphism is quasi-finite. In this paper, we strengthen McMullen's theorem by showing that the multiplier spectrum morphism is generically injective. This answers a question of McMullen and Poonen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15382 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The multiplier spectrum morphism is generically injective Ji, Zhuchao Xie, Junyi Dynamical Systems Algebraic Geometry In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexible Lattès family, the multiplier spectrum morphism is quasi-finite. In this paper, we strengthen McMullen's theorem by showing that the multiplier spectrum morphism is generically injective. This answers a question of McMullen and Poonen. |
| title | The multiplier spectrum morphism is generically injective |
| topic | Dynamical Systems Algebraic Geometry |
| url | https://arxiv.org/abs/2309.15382 |