Uniform unlikely intersections for unicritical polynomials
Abstract
Fix $d\geq2$, and consider the family $f_{t}(z)=z^{d}+t$ of polynomials parameterized by $t\in\mathbb{C}$. In this article, we will show that there exists a constant $C(d)$ such that for any $a,b\in\mathbb{C}$ with $a^{d}\neq b^{d}$, the number of $t\in\mathbb{C}$ such that $a$ and $b$ are both preperiodic for $f_{t}$ is at most $C(d)$.
Fields of Study & Subjects
Meromorphic and Entire Functions
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Épijournal de Géométrie Algébrique
- Volume
- Volume 10
- Publication date
- 9 September 2026
- Language
- EN