Invariant Varieties of Periodic Points for Some Higher Dimensional Integrable Maps

Abstract

By studying various rational integrable maps on \\hatC^d with p invariants, we show that periodic points form an invariant variety of dimension ≥p for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: “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.”