Birational automorphisms of positive entropy and their regularizations

An interesting class of automorphisms are automorphisms of positive entropy. By the Gromov and Yomdin theorem if we consider the action of such automorphism by pull-back on the group $H^{1,1}$ it has an eigenvalue greater that 1. In dimension 3 there exists just one known example of primitive regular automorphism with positive entropy of rational variety. Also there exist several birational automorphisms of P^3 with a correctly defined action on $H^{1,1}$ with an eigenvalue greater than 1. I will describe one of these automorphisms and show that it could not be regularized.