Rational maps with integer multipliers

Xavier Buff (1) , Thomas Gauthier (2) , Valentin Huguin , Jasmin Raissy (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMO - Laboratoire de Mathématiques d'Orsay
3 IMB - Institut de Mathématiques de Bordeaux

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 Lattès 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.

Domaines: Mathématiques [math]

Xavier Buff, Thomas Gauthier, Valentin Huguin, Jasmin Raissy. Rational maps with integer multipliers. 2022. ⟨hal-03888827⟩