Birational automorphism groups and the movable cone theorem for   Calabi-Yau manifolds of Wehler type via universal Coxeter groups
  Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds $X$ of arbitrary dimension $n$, for which $\Bir(X)$ is infinite and the Kawamata-Morrison movable cone conjecture is satisfied. For this family, the movable cone is explicitly described; it's fractal nature is related to limit sets of Kleinian groups and to the Apollonian Gasket. Then, we produce explicit examples of (biregular) automorphisms with positive entropy on some Calabi-Yau manifolds. 
Serge Cantat, Keiji Oguiso
math.AG math.DS