# Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks

 Title: Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks Author: McMullen, Curtis T. Citation: 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. Full Text & Related Files: McMullen_SalemNumberSiegel.pdf (1.679Mb; PDF) 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. Published Version: doi:10.1515/crll.2002.036 Other Sources: http://www.math.harvard.edu/~ctm/papers/index.html Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446014 Downloads of this work:

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