Dynamics on projective K3 surfaces: Herman rings

We construct an automorphism of a smooth projective K3 surface with positive topological entropy and a non-empty Fatou set. The Fatou set contains invariant domains biholomorphic to a product of two annuli, on which the automorphism is conjugate to an irrational rotation. The proof uses KAM theory. We construct a real K3 surface whose real locus is a union of two tori, and on each torus the automorphism is conjugate to a Diophantine rotation. These conjugacies then extend holomorphically to the invariant domains. This talk is based on arXiv:2609.38013.