Multiplier scales of a sequence of rational maps
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912675711156224 |
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| author | Gong, Chen |
| author_facet | Gong, Chen |
| contents | We analyze the behavior of multipliers of a degenerating sequence of complex rational maps. We show either most periodic points have uniformly bounded multipliers, or most of them have exploding multipliers at a common scale. We further explore the set of scales induced by the growth of multipliers. Using Ahbyankar's theorem, we prove that there can be at most 2d-2 such non-trivial multiplier scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplier scales of a sequence of rational maps Gong, Chen Dynamical Systems Algebraic Geometry Complex Variables We analyze the behavior of multipliers of a degenerating sequence of complex rational maps. We show either most periodic points have uniformly bounded multipliers, or most of them have exploding multipliers at a common scale. We further explore the set of scales induced by the growth of multipliers. Using Ahbyankar's theorem, we prove that there can be at most 2d-2 such non-trivial multiplier scales. |
| title | Multiplier scales of a sequence of rational maps |
| topic | Dynamical Systems Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2510.25029 |