The nature of manifolds of periodic points for higher dimensional   integrable maps II
  We study periodicity conditions of a rational map on $\bm{C}^d$ with $p$ invariants and show that a set of isolated periodic points and an algebraic variety of finife dimension do not exist in one map simultaneously if $p\ge d/2$. We also discuss in detail how the transition takes place between them. 
Satoru Saito, Noriko Saitoh