  The aim of this paper is to give necessary and sufficient conditions for an
integral polynomial to be the characteristic polynomial of a semi-simple
isometry of some even unimodular lattice of given signature. This result has
applications applications to automorphisms of K3 surfaces; in particular, we
show that every Salem number of degree 4, 6, 8,1 2, 14 or 16 is the dynamical
degree of an automorphism of a non-projective K3 surface.
