Critical points of the multiplier map for the quadratic family

2019/02/27 by Анна Белова, Belova, Anna, Igors Gorbovickis +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1902.10444

openalex publication_date 2019/02/27 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

The multiplier λ_n of a periodic orbit of period n can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials p_c(z)=z²+c. We provide a numerical algorithm for computing critical points of this function (i.e., points where the derivative of the multiplier with respect to the complex parameter c vanishes). We use this algorithm to compute critical points of λ_n up to period n=10.

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