Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points
Dynamical Systems
2026-07-21 v1
Abstract
Let be an algebraically closed, complete non-Archimedean field of residue characteristic . Let be a polynomial of degree at least over which does not have potential good reduction. We prove that if is any other polynomial with the same Julia set, then and must be dynamically related. As a consequence, we show that for any two complex polynomials of degree at least , either their sets of preperiodic points coincide, or the number of their common preperiodic points is uniformly bounded above by a constant depending only on the degrees, thereby answering a conjecture of DeMarco--Krieger--Ye for polynomials. We also establish relative results, allowing us to prove special cases of the DeMarco--Mavraki conjecture.
Cite
@article{arxiv.2607.19252,
title = {Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points},
author = {Chen Gong and Jit Wu Yap},
journal= {arXiv preprint arXiv:2607.19252},
year = {2026}
}
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