Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks

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Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks

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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.
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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

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  • FAS Scholarly Articles [7218]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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