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.'}
Categories: math-ph math.MP