arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1506.02477math.ATmath.GR
收藏

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

Jonas Deré

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑