Quadratic rational maps with integer multipliers

Valentin Huguin

Published 2021-07-15Version 1

In this article, we prove that every quadratic rational map whose multipliers all lie in the ring of integers of a given imaginary quadratic field is a power map, a Chebyshev map or a Latt\`{e}s map. In particular, this provides some evidence in support of a conjecture by Milnor concerning rational maps whose multipliers are all integers.