# Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks

@article{McMullen2002DynamicsOK,
title={Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks},
author={Curtis T. McMullen},
journal={Crelle's Journal},
year={2002},
volume={2002},
pages={201-233}
}
• C. McMullen
• Published 8 January 2002
• Mathematics
• Crelle's Journal
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…
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