标题： 高维可积映射的周期点流形的性质 显示英文标题

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

摘要： 通过研究带有$p$不变量的$\bm{C}^d$上有理映射的周期点，我们证明当周期性条件为“完全相关”时，它们形成一个维数为$p$的不变代数簇，而当条件为“不相关”时，它们则是一组孤立点。 我们在可积映射的情况下给出了许多不变代数簇的例子。 此外，我们证明在一个映射中，不变代数簇和一组孤立点不能同时存在。 显示英文摘要

摘要： 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.