Invariant varieties of periodic points for some higher dimensional integrable maps

Details Invariant varieties of periodic points for some higher dimensional integrable maps Invariant varieties of periodic points for some higher dimensional integrable maps

2006-10-25

arxiv.org/abs/math-ph/0610069v2

Physics

Mathematical Physics

24 pages

Scientific paper

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.'}

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