Some Applications of Dynamical Belyi Polynomials

2021/09/07 by Jacqueline Anderson, Anderson, Jacqueline, Michelle Manes +3
Mathematics · #11G #37P05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.03339

openalex publication_date 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions for post-critically finite polynomials to have persistent bad reduction at a given prime. We also answer in the negative a pair of questions posed by Silverman about conservative polynomials. Our proofs rely on conservative dynamical Belyi polynomials as exemplars of PCF (resp. conservative) maps.

Related

• Dynamical Belyi maps
• On postcritically finite polynomials, part 1: critical portraits
• Integrality and Thurston Rigidity for Bicritical PCF Polynomials
• A remark on post-critically finite compositions of polynomials
• Iterates of post-critically finite polynomials of the form \boldsymbolx^d+c