Equidistribution of critical points of the multipliers in the quadratic\n family

2019/02/28 by Tanya Firsova, Firsova, Tanya, Igors Gorbovickis +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1903.00062

openalex publication_date 2019/02/28 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

A parameter c₀\∈ mathbb C in the family of quadratic polynomials\nf_c(z)=z²+c is a critical point of a period n multiplier, if the map\nf_c0 has a periodic orbit of period n, whose multiplier, viewed as a\nlocally analytic function of c, has a vanishing derivative at c=c₀. We\nprove that all critical points of period n multipliers equidistribute on the\nboundary of the Mandelbrot set, as n\→\∞.\n

Related

• Accumulation set of critical points of the multipliers in the quadratic family
• Critical points of the multiplier map for the quadratic family
• Quadratic polynomials, multipliers and equidistribution
• Multipliers of periodic orbits of quadratic polynomials and the parameter plane
• Critical orbits of polynomials with a periodic point of specified\n multiplier