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hal-00143816, version 2

Periodicity of certain piecewise affine planar maps

Shigeki Akiyama () 1, Horst Brunotte () 2, Attila Petho () 3, Wolfgang Steiner () 4

Abstract: We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. Using these maps, we prove for $\lambda\in\{\frac{\pm1\pm\sqrt5}2,\pm\sqrt2,\pm\sqrt3\}$ that all integer sequences $(a_k)_{k\in\mathbb Z}$ satisfying $0\le a_{k-1}+\lambda a_k+a_{k+1}<1$ are periodic.

  • 1:  Department of Mathematics
  • Niigata University
  • 2:  Düsseldorf
  • Düsseldorf
  • 3:  Institute of Mathematics and Computer Science
  • University of Debrecen
  • 4:  Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
  • CNRS : UMR7089 – Université Paris VII - Paris Diderot
 
  • hal-00143816, version 2
  • http://hal.archives-ouvertes.fr/hal-00143816
  • oai:hal.archives-ouvertes.fr:hal-00143816
  • From: Wolfgang Steiner <>
  • Submitted on: Monday, 30 July 2007 11:18:42
  • Updated on: Monday, 30 July 2007 11:24:59