Discretized rotation has infinitely many periodic orbits
arXiv:1206.3868 · doi:10.1088/0951-7715/26/3/871
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.
Revised after referee reports, and added a quantitative statement