Work

Quadratic polynomials, multipliers and equidistribution

Year: 2013

Type: preprint

Abstract: Given a sequence of complex numbers ρ_n, we study the asymptotic distribution of the sets of parameters c ε C such that the quadratic maps z^2 +c has a cycle of period n and multiplier ρ_n. Assume 1/n.log|ρ_n| tends to L. If L {\leq} log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2 they equidistribute on the equipotential of the Mandelbrot set of level 2L - 2 log 2.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.1306.2736

Authors: Buff, Xavier, Gauthier, Thomas

Institutions: Institut de Mathématiques de Toulouse, Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4297957115

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