Distribution of polynomials with cycles of a given multiplier

DOI10.1215/00277630-2010-016zbMath1267.37049arXiv0907.0011OpenAlexW1664311014MaRDI QIDQ5391074

Giovanni Bassanelli, François Berteloot

Publication date: 5 April 2011

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0011

zbMATH Keywords

rational mapsholomorphic familiesbifuraction currents

Mathematics Subject Classification ID

Currents (32U40) General pluripotential theory (32U15)

Related Items

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 ⋮ On the geometry of bifurcation currents for quadratic rational maps ⋮ Distribution of postcritically finite polynomials ⋮ Hyperbolic components of rational maps: quantitative equidistribution and counting ⋮ Hyperbolicity and Bifurcations in holomorphic families of polynomial skew products ⋮ Distribution of postcritically finite polynomials III: Combinatorial continuity ⋮ Equidistribution of critical points of the multipliers in the quadratic family ⋮ Random walks, Kleinian groups, and bifurcation currents ⋮ The bifurcation measure has maximal entropy ⋮ Quadratic polynomials, multipliers and equidistribution ⋮ Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current

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