A geometric approach to singularity confinement and algebraic entropy
  A geometric approach to the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an automorphism of a certain rational surface and can therefore be considered to be the action of an extended Weyl group of indefinite type. A method to calculate its algebraic entropy by using the theory of intersection numbers is presented. 
Tomoyuki Takenawa