Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy
Serge CantatUniversité de Rennes 1, France
Christophe DupontUniversité de Rennes 1, France
We classify complex projective surfaces with an automorphism of positive entropy for which the unique measure of maximal entropy is absolutely continuous with respect to the Lebesgue measure. As a byproduct, if is a K3 surface and is not a Kummer surface, the periodic points of are equidistributed with respect to a probability measure which is singular with respect to the canonical volume of . The proof is based on complex algebraic geometry and Hodge theory, Pesin’s theory and renormalization techniques. A crucial argument relies on a new compactness property of entire curves parametrizing the invariant manifolds of the automorphism.
Cite this article
Serge Cantat, Christophe Dupont, Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy. J. Eur. Math. Soc. 22 (2020), no. 4, pp. 1289–1351DOI 10.4171/JEMS/946