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Every Salem numbers of degree 4,6,8,12,14 or 16 is the dynamical degree of anautomorphism of a non-projective K3 surface. We define a notion of signature ofan automorphism, and use it to give a necessary and sufficient condition forSalem numbers of degree 10 and 18 to be realized as the dynamical degree ofsuch an automorphism. The first part of the paper contains results onisometries of lattices.

Automorphisms of K3 surfaces, signatures, and isometries of lattices