Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
View/ Open
Author
Published Version
https://doi.org/10.1515/crll.2002.036Metadata
Show full item recordCitation
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.Other Sources
http://www.math.harvard.edu/~ctm/papers/index.htmlTerms 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#LAACitable link to this page
http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446014
Collections
- FAS Scholarly Articles [18256]
Contact administrator regarding this item (to report mistakes or request changes)