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Let be a compact K"ahler manifold of dimension and a pseudo-automorphism. If the first dynamical degree is a Salem number, we show that either or . In particular, if then . We use this to show that if is a complex 3-torus and is an automorphism of with , then has a non-trivial equivariant holomorphic fibration if and only if is a Salem number. If is a complex 3-torus having an automorphism with but is not a Salem number, then the Picard number of must be 0,3 or 9, and all these cases can be realized.

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