AUTOMORPHISMS OF COMPACT KAHLER MANIFOLDS WITH SLOW DYNAMICS

We study automorphisms of compact Kahler manifolds having slow dynamics. Adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions 2 and 3. We prove that every automorphism with sublinear derivative growth is an isometry; a counter-example is given in the context, answering negatively a question of Artigue, Carrasco-Olivera, and Monteverde in [Acta Math. Hungar. 152 (2017), pp. 140-149] on polynomial entropy. We also study minimal automorphisms of surfaces with respect to the Zariski or euclidean topology.