AI 中文总结
本文构造了射影K3曲面上具有正拓扑熵和非空Fatou集的自同构，其不变域为Herman环的二维类比，解答了McMullen和Cantat的开放问题。
AI 中文摘要
我们构造了一个光滑射影K3曲面的自同构，其具有正拓扑熵和非空Fatou集。该Fatou集包含与两个环带乘积双全纯等价的不变域。在每个域上，该自同构全纯共轭于无不动点的无理旋转。这些域是Herman环的二维类比。该构造回答了McMullen在2002年提出的一个问题，以及Cantat在2018年ICM演讲中提出的若干问题。
英文摘要
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 products of two annuli. On each domain, the automorphism is holomorphically conjugate to a fixed-point-free irrational rotation. These domains are two-dimensional analogues of Herman rings. The construction answers a question posed by McMullen in 2002 and several questions posed by Cantat in his 2018 ICM address.
Comments25 pages, 1 figure; comments are welcome!
