Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
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CitationMcMullen, Curtis T. 2002. Dynamics on K3 surfaces: Salem numbers and Siegel disks. Journal fur die Reine und Angewandte Mathematik 2002(545): 201–233. Revised 2005.
AbstractThis 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 results from transcendence theory.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:3446014
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