Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy

Serge Cantat (1) , Christophe Dupont (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

Mots clés: invariant current; measure of maximal entropy; entire curve; Kummer example; holomorphic automorphism; renormalization

Domaines: Systèmes dynamiques [math.DS]

Serge Cantat, Christophe Dupont. Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy. Journal of the European Mathematical Society, 2020, 22 (4), pp.1289-1351. ⟨10.4171/JEMS/946⟩. ⟨hal-01071491⟩