动态典范高度与有限树
Dynamical Canonical Heights and Finite Trees
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中文总结 AI 辅助
本文针对素数幂次的特定多项式，基于Dimitrov的思路，通过构建有限树并结合核心熵分析，建立了游荡点典范高度的平方级衰减下界。
中文摘要 AI 辅助
我们针对游荡点的典范高度建立了下界，其衰减速率为域度的平方。我们的方法与结果适用于素数幂次的中心化、后临界有限双曲多项式，这类多项式的系数为代数整数。我们的方法最终源于Dimitrov的一个想法，该想法促成了他对Schinzel–Zassenhaus猜想的证明。该高度下界由阿基米德位处局部典范高度的下界推导得出。在先前的工作中，作者们使用了Dubinin关于星形树超限直径的结果。本文中，我们开发工具以界定复平面上更一般有限树的超限直径，利用后临界有限多项式的Hubbard树构建这些树，并借助Thurston的核心熵概念分析Hubbard树的组合性质。
英文摘要
We establish lower bounds for the canonical height of a wandering point that decays like the square of the field degree. Our methods and results apply to centered, postcritically finite, hyperbolic polynomials of prime power degree whose coefficients are algebraic integers. Our approach is ultimately inspired by an idea of Dimitrov that led to his proof of the Schinzel--Zassenhaus Conjecture. The height lower bound is derived from the lower bound of the local canonical height at an archimedean place. In previous work, the authors used a result of Dubinin on the transfinite diameter of a star-shaped tree. In this paper, we develop tools to bound the transfinite diameter of more general finite trees in the complex plane. We construct these trees using the Hubbard tree of a postcritically finite polynomial. Thurston's notion of core entropy helps us analyze combinatorial properties of the Hubbard tree.
