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PreprintCC BY 4.0arXiv

Dynamics on projective K3 surfaces: Herman rings

  • Junyu Cao
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026dynamics,
  title = {{Dynamics on projective K3 surfaces: Herman rings}},
  author = {Junyu Cao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38013},
  eprint = {2609.38013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38013},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dynamics on projective K3 surfaces: Herman rings
AU  - Junyu Cao
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38013
UR  - https://arxiv.org/abs/2609.38013
AB  - 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.
ER  -