On the cohomological action of automorphisms of compact K\"ahler threefolds

Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact K\"ahler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most as $cn^4$; in the general case, we give a description of the spectrum of $f^*$, and bounds on the possible conjugates over $\mathbb Q$ of the dynamical degrees $\lambda_1(f),\lambda_2(f)$. Examples on complex tori show the optimality of the results.