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The goal of this paper is the exact computation of the degrees$\text{deg}(f^n)$ of the iterates of birational maps $f: \mathbb{P}^N\dashrightarrow \mathbb{P}^N$. In the preceding companion paper, a new methodhas been proposed based on the use of indices of polynomials associated to thelocal blow-ups used to resolve contractions of hypersurfaces by $f$, and on thecontrol of the factorization of pull-backs of polynomials. This leads torecurrence relations for the degrees and the indices. We apply this method toseveral illustrative examples in three dimensions. These examples demonstratethe flexibility of the method which, in particular, does not require theconstruction of an algebraically stable lift of $f$, unlike the previouslyknown methods based on the Picard group.

Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups II. 3D examples