Birational maps with transcendental dynamical degree

Abstract

We give examples of birational selfmaps of ${\mathbb{P}}^d,d\ge 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.

To appear in Proc. Lond. Math. Soc