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Wild automorphisms of compact complex spaces of lower dimensions. (arXiv:2211.12245v2 [math.AG] UPDATED)

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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 must be 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 K\"ahler threefolds or fourfolds, and
generalise the results of Oguiso--Zhang from the projective case to the
K\"ahler case.

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