Publication: Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
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Date
2002
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Walter de Gruyter
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McMullen, 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.
Abstract
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 results from transcendence theory.
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