Uniform unlikely intersections for unicritical polynomials
Hang Fu

TL;DR
This paper establishes a uniform bound on the number of parameters for which two distinct points are simultaneously preperiodic under a family of unicritical polynomials, revealing a deep intersection property.
Contribution
It proves the existence of a universal constant C(d) bounding the number of such parameters for any pair of points with distinct d-th powers.
Findings
Existence of a uniform bound C(d) for preperiodic intersections.
Bound applies to all pairs with a^d ≠ b^d.
Results contribute to understanding unlikely intersections in polynomial families.
Abstract
Fix and let be the family of polynomials parameterized by . In this article, we will show that there exists a constant such that for any with , the number of such that and are both preperiodic for is at most .
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Taxonomy
TopicsMeromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals
