Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks

  title={Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks},
  author={Curtis T. McMullen},
  journal={Crelle's Journal},
  • C. McMullen
  • Published 8 January 2002
  • Mathematics
  • Crelle's Journal
This paper presents the first examples of K3 surface automorphisms \(f : X \rightarrow X\) with Siegel disks (domains on which f acts by an irrational rotation). The set of such examples is countable, and the surface \(X\) must be non-projective to carry a Siegel disk. These automorphisms are synthesized from Salem numbers of degree 22 and trace −1, which play the role of the leading eigenvalue for \(f*|H^2(X)\). The construction uses the Torelli theorem, the Atiyah-Bott fixed-point theorem and… 

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