仿射亚零流形自同态的周期点和最终周期点
Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms
摘要：
本文研究了仿射亚零流形自同态的周期点和最终周期点。一方面，我们给出了次零流形上的点是（最终）周期的一个充分条件。用这种方法我们证明了如果仿射亚零流形自同态有周期点，那么它的周期点的集合构成流形的稠密子集。另一方面，我们推出了最终周期点的一个必要条件，从该条件出发，对任意仿射次nilmanifold自同态的最终周期点的集合给出了完整的描述。
英文摘要：
In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we show that if an affine infra-nilmanifold endomorphism has a periodic point, then its set of periodic points forms a dense subset of the manifold. On the other hand, we deduce a necessary condition for eventually periodic points from which a full description of the set of eventually periodic points follows for an arbitrary affine infra-nilmanifold endomorphism.
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