Critical orbits of polynomials with a periodic point of specified\n multiplier

2017/06/16 by Patrick Ingram, Ingram, Patrick
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1706.05352

openalex publication_date 2017/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Answering a question posed by Adam Epstein, we show that the collection of\nconjugacy classes of polynomials admitting a parabolic fixed point and at most\none infinite critical orbit is a set of bounded height in the relevant moduli\nspace. We also apply the methods over function fields to draw conclusions about\nalgebraically parametrized families, and prove an analogous result for\nquadratic rational maps.\n

Related

• Parameterizing degree n polynomials by multipliers of periodic orbits
• Critical points of the multiplier map for the quadratic family
• Multipliers of periodic orbits of quadratic polynomials and the parameter plane
• Multipliers of periodic orbits in spaces of rational maps
• Accumulation set of critical points of the multipliers in the quadratic family