A characterization of the periods of periodic points of 1-norm nonexpansive maps

• Bas Lemmens ^[1] ; Michael Scheutzow ^[1]
  1. [1] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 9, Nº. 4, 2003, págs. 557-578
• Idioma: inglés
• DOI: 10.1007/s00029-003-0342-6
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• Resumen

  • In this paper the set of minimal periods of periodic points of 1-norm nonexpansive maps f:Rn→Rn is studied. This set is denoted by R(n). The main goal is to present a characterization of R(n) by arithmetical and combinatorial constraints. More precisely, it is shown that R(n)=Q′(2n) , where Q′(2n) denotes the set of periods of restricted admissible arrays on 2n symbols. The important point of this equality is that Q′(2n) is determined by arithmetical and combinatorial constraints only, and that it can be computed in finite time. By using this equality the set R(n) is computed for 1≤n≤10 . Furthermore it is shown that the largest element ψ(n) of R(n) satisfies: logψ(n)∼2nlogn−−−−−−√.