skip to main content


Search for: All records

Creators/Authors contains: "Ye, Hexi"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Let \begin{document}$ f_c(z) = z^2+c $\end{document} for \begin{document}$ c \in {\mathbb C} $\end{document}. We show there exists a uniform upper bound on the number of points in \begin{document}$ {\mathbb P}^1( {\mathbb C}) $\end{document} that can be preperiodic for both \begin{document}$ f_{c_1} $\end{document} and \begin{document}$ f_{c_2} $\end{document}, for any pair \begin{document}$ c_1\not = c_2 $\end{document} in \begin{document}$ {\mathbb C} $\end{document}. The proof combines arithmetic ingredients with complex-analytic: we estimate an adelic energy pairing when the parameters lie in \begin{document}$ \overline{\mathbb{Q}} $\end{document}, building on the quantitative arithmetic equidistribution theorem of Favre and Rivera-Letelier, and we use distortion theorems in complex analysis to control the size of the intersection of distinct Julia sets. The proofs are effective, and we provide explicit constants for each of the results.

     
    more » « less