The third smallest Salem number in automorphisms of K3 surfaces

Details The third smallest Salem number in automorphisms of K3 surfaces The third smallest Salem number in automorphisms of K3 surfaces

2009-05-14

arxiv.org/abs/0905.2396v2

Mathematics

Algebraic Geometry

22 pages, many typos in formulas, values and in english are corrected. Main results are unchanged

Scientific paper

We realize the logarithm of the third smallest known Salem number as the topological entropy of a K3 surface automorphism with a Siegel disk and a pointwisely fixed curve at the same time. We also show the logarithm of the Lehmer number, the smallest known Salem number, is not realizable as the topological entropy of any Enriques surface automorphism. These results are entirely inspired by McMullen's works and Mathematica programs.

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