Paper

Discretized rotation has infinitely many periodic orbits

and

Published 13 February 2013 • © 2013 IOP Publishing Ltd & London Mathematical Society
, , Citation Shigeki Akiyama and Attila Pethő 2013 Nonlinearity 26 871 DOI 10.1088/0951-7715/26/3/871

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Author e-mails

akiyama@math.tsukuba.ac.jp

petho.attila@inf.unideb.hu

Author affiliations

1 Institute of Mathematics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8571 Japan

2 Department of Computer Science, University of Debrecen, PO Box 12, H-4010 Debrecen, Hungary

Dates

  1. Received 15 August 2012
  2. Published

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0951-7715/26/3/871

Abstract

For a fixed λ ∈ (−2, 2), we study a family of discretized rotation on ${\mathbb Z}^2$ defined by

We prove that this reversible dynamics has infinitely many periodic orbits.

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