English

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.

Keywords

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

R2 v1 2026-06-21T21:21:07.701Z