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Quantitative equidistribution of angles of multipliers

Volume 257 / 2022

Yan Mary He, Hongming Nie Fundamenta Mathematicae 257 (2022), 95-113 MSC: Primary 37F15; Secondary 37F10. DOI: 10.4064/fm63-7-2021 Published online: 3 January 2022

Abstract

We study angles of multipliers of repelling cycles for hyperbolic rational maps in $\mathbb {C}(z)$. For a fixed $K \gg 1$, we show that nearly every interval of length $2\pi /K$ in $(-\pi ,\pi ]$ contains a multiplier angle with the property that the absolute value of the multiplier is bounded above by a polynomial in $K$.

Authors

  • Yan Mary HeDepartment of Mathematics
    University of Toronto
    Toronto M5S 2E4, Canada
    e-mail
  • Hongming NieFacultad de Matemáticas
    Pontificia Universidad Católica de Chile
    Santiago, Chile
    e-mail

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