Automorphismes loxodromiques de surfaces abéliennes réelles

Abstract

— We study dynamical degree > 1 real automorphisms of compact complex surfaces with a real structure. We show that a surface with such an automorphism is necessarily projective. We classify real abelian surfaces into eight types, according to the number of connected components of the real part and the simplicity of the underlying complex abelian surface. For each type, we determine the set of values of dynamical degrees which can be realized by real automorphisms. We also prove that the minimum dynamical degree on a complex K3 surface can not be realized on a real K3 surface.