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arXiv · 2510.25029

Multiplier scales of a sequence of rational maps

Chen Gong
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Abstract

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.

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Chen Gong. 2025-10-28. Multiplier scales of a sequence of rational maps. https://arxiv.org/abs/2510.25029

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