arXiv Analytics

Sign in

arXiv:1206.3868 [math.DS]AbstractReferencesReviewsResources

Discretized rotation has infinitely many periodic orbits

Shigeki Akiyama, Attila Pethoe

Published 2012-06-18, updated 2012-12-20Version 3

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.

Comments: Revised after referee reports, and added a quantitative statement
Categories: math.DS, math.NT
Subjects: 37E15, 37E05, 11A63
Related articles: Most relevant | Search more
arXiv:math/9907003 [math.DS] (Published 1999-07-01, updated 2001-04-26)
Arithmetic and growth of periodic orbits
arXiv:0904.2719 [math.DS] (Published 2009-04-17)
Existence of periodic orbits for geodesible vector fields on closed 3-manifolds
arXiv:0705.2361 [math.DS] (Published 2007-05-16)
Periodic orbits in the case of a zero eigenvalue

Links

Toolbox