WILD AUTOMORPHISMS OF COMPACT COMPLEX SPACES OF LOWER DIMENSIONS

An automorphism of a compact complex space is called wild in the sense of Reichstein-Rogalski-Zhang if there is no non-trivial proper invariant analytic subset. We show that a compact complex surface admitting a wild automorphism is either a complex torus or an Inoue surface of certain type, and this wild automorphism has zero entropy. As a by-product of our argument, we obtain new results about the automorphism groups of Inoue surfaces. We also study wild automorphisms of compact Ka & BULL;hler threefolds or fourfolds, and generalise the results of Oguiso-Zhang from the projective case to the Ka & BULL;hler case.