Pseudoautomorphisms with invariant elliptic curves
  We describe an explicit method for constructing pseudo-automorphisms of a space $X$ which is obtained by blowing up points of $P^k$ (or a product $P^k \times \cdots \times P^k$). The centers of blowup are chosen to lie on an elliptic normal curve and are determined using the arithmetic on the curve. These pseudo-automorphism have dynamical degree greater than $1$. 
Eric Bedford, Jeffery Diller, Kyounghee Kim
math.DS math.AG