  We study positive entropy birational automorphisms of threefolds. We identify
some conditions which imply that such an automorphism is non-regularizable. We
show that this criterion applies in the example of a positive entropy
birational automorphism of $\mathbb{P}^3$ constructed by J. 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.
