The nature of manifolds of periodic points for higher dimensional integrable maps
Satoru Saito, Noriko Saitoh
Abstract
By studying periodic points for rational maps on Cd with p invariants, we show that they form an invariant variety of dimension p if the periodicity conditions are `fully correlated', and a set of isolated points if the conditions are `uncorrelated'. We present many examples of the invariant varieties in the case of integrable maps. Moreover we prove that an invariant variety and a set of isolated points do not exist in one map simultaneously.
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