Rational maps with integer multipliers

Xavier Buff, Thomas Gauthier, Valentin Huguin, Jasmin Raissy

Published 2022-12-07Version 1

Let $O_K$ be the ring of integers of an imaginary quadratic field. Recently, Zhuchao Ji and Junyi Xie proved that rational maps whose multipliers at all periodic points belong to $O_K$ are power maps, Chebyshev maps or Latt\`es maps. Their proof relies on a non-archimedean result by Benedetto, Ingram, Jones and Levy. In this note, we show that one may avoid using this non-archimedean result by considering a differential equation instead.