Quadratic polynomials, multipliers and equidistribution

DOI10.1090/S0002-9939-2015-12506-3zbMath1334.37038arXiv1306.2736OpenAlexW2964321201MaRDI QIDQ5246927

Thomas Gauthier, Xavier Buff

Publication date: 22 April 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2736

zbMATH Keywords

Green functionperiodic pointmultiplierMandelbrot set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (11)

Parabolic bifurcation loci in the spaces of rational functions ⋮ Distribution of postcritically finite polynomials. II: Speed of convergence ⋮ Equidistribution towards the bifurcation current. I: Multipliers and degree \(d\) polynomials ⋮ Critical Points of the Multiplier Map for the Quadratic Family ⋮ Hyperbolic components of rational maps: quantitative equidistribution and counting ⋮ An a priori bound for rational functions on the Berkovich projective line ⋮ Hyperbolicity and Bifurcations in holomorphic families of polynomial skew products ⋮ The Mandelbrot set is the shadow of a Julia set ⋮ Distribution of postcritically finite polynomials III: Combinatorial continuity ⋮ Equidistribution of critical points of the multipliers in the quadratic family ⋮ Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current

Cites Work

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• The dynamics of complex polynomials and automorphisms of the shift
• Geometry and Dynamics of Quadratic Rational Maps
• On biaccessible points of the Mandelbrot set
• Distribution of polynomials with cycles of a given multiplier

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