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In this paper, we study the periodic and eventually periodic points of affineinfra-nilmanifold endomorphisms. On the one hand, we give a sufficientcondition for a point of the infra-nilmanifold to be (eventually) periodic. Inthis way we show that if an affine infra-nilmanifold endomorphism has aperiodic point, then its set of periodic points forms a dense subset of themanifold. On the other hand, we deduce a necessary condition for eventuallyperiodic points from which a full description of the set of eventually periodicpoints follows for an arbitrary affine infra-nilmanifold endomorphism.

Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms