Multiplier scales of a sequence of rational maps
Dynamical Systems
2025-10-30 v1 Algebraic Geometry
Complex Variables
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.
Cite
@article{arxiv.2510.25029,
title = {Multiplier scales of a sequence of rational maps},
author = {Chen Gong},
journal= {arXiv preprint arXiv:2510.25029},
year = {2025}
}