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Invariant varieties of periodic points for some higher dimensional integrable maps

Satoru Saito·Noriko Saitoh
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Abstract

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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Satoru Saito, Noriko Saitoh. 2006-12-28. Invariant varieties of periodic points for some higher dimensional integrable maps. https://doi.org/10.1143/jpsj.76.024006

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