Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 721736, 15 pages
doi:10.1155/2010/721736
Research Article

Eventually Periodic Points of Infra-Nil Endomorphisms

Ku Yong Ha, Hyun Jung Kim, and Jong Bum Lee

Department of Mathematics, Sogang University, Seoul 121-742, South Korea

Received 14 August 2009; Revised 26 December 2009; Accepted 19 February 2010

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2010 Ku Yong Ha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Hyperbolic toral automorphisms provide important examples of chaotic dynamical systems. Generalizing automorphisms on tori, we study (infra-)nil endomorphisms defined on (infra-)nilmanifolds. In particular, we show that every infra-nil endomorphism has dense eventually periodic points.