Pseudo-automorphisms with no invariant foliation

Eric Bedford (1) , Serge Cantat (2) , Kyounghee Kim (3)

1 LRS - Laboratoire de Réactivité de Surface
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Greeneridge Sciences

We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this provides a negative answer to a question of Guedj. On our way, we develop several techniques to study foliations which are invariant under birational transformations.

Mots clés: invariant foliation; singular foliation; cohomologically nonhyperbolic; regular birational map; rational 3-folds; Pseudo-automorphism

Domaines: Systèmes dynamiques [math.DS]

Eric Bedford, Serge Cantat, Kyounghee Kim. Pseudo-automorphisms with no invariant foliation. Journal of modern dynamics, 2014, 8 (2), pp.221-250. ⟨10.3934/jmd.2014.8.221⟩. ⟨hal-01091518⟩