Discretized rotation has infinitely many periodic orbits
Dynamical Systems
2015-06-05 v3 Number Theory
Abstract
For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.
Cite
@article{arxiv.1206.3868,
title = {Discretized rotation has infinitely many periodic orbits},
author = {Shigeki Akiyama and Attila Pethoe},
journal= {arXiv preprint arXiv:1206.3868},
year = {2015}
}
Comments
Revised after referee reports, and added a quantitative statement