Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms
Algebraic Topology
2015-06-09 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1506.02477,
title = {Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms},
author = {Jonas Deré},
journal= {arXiv preprint arXiv:1506.02477},
year = {2015}
}
Comments
18 pages