We study birational automorphisms of threefolds which have positive algebraic entropy. We identify some conditions which imply that such an automorphism is non-regularizable. We show that this criterion applies in the example of a birational automorphism of $ \mathbb{P}^3 $ of positive algebraic entropy constructed by Blanc, thus showing that for a general choice of parameters it is non-regularizable. Additionally, we establish a criterion which proves that the automorphism in this example does not preserve a structure of a fibration over a surface.
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