The nature of manifolds of periodic points for higher dimensional integrable maps

Details The nature of manifolds of periodic points for higher dimensional integrable maps The nature of manifolds of periodic points for higher dimensional integrable maps

2005-08-31

arxiv.org/abs/math-ph/0508063v2

Physics

Mathematical Physics

18 pages, content changed to improve

Scientific paper

By studying periodic points for rational maps on $\bm{C}^d$ 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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