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arXiv · 1506.02477

Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms

Jonas Deré
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Abstract

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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Jonas Deré. 2015-06-08. Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. https://arxiv.org/abs/1506.02477

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