  By studying various rational integrable maps on $\mathbf{\hat C}^d$ with $p$
invariants, we show that periodic points form an invariant variety of dimension
$\ge p$ for each period, in contrast to the case of nonintegrable maps in which
they are isolated. We prove the theorem: {\it `If there is an invariant variety
of periodic points of some period, there is no set of isolated periodic points
of other period in the map.'}
