Families of transitive maps on R with horizontal asymptotes

• Bladismir Leal ^[1] ; Guelvis Mata ^[1] ; Sergio Muñoz ^[2]
  1. [1] Universidad Nacional de Chimborazo

     Universidad Nacional de Chimborazo

     Riobamba, Ecuador

     
  2. [2] Universidade do Estado do Rio de Janeiro

     Universidade do Estado do Rio de Janeiro

     Brasil

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 2, 2018, págs. 375-387
• Idioma: inglés
• DOI: 10.33044/revuma.v59n2a08
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• Resumen

  • We will prove the existence of a class of transitive maps on the real line R, with a discontinuity and horizontal asymptotes, whose set of periodic orbits is dense in R; that is, a class of chaotic families. In addition, we will show a rare phenomenon: the existence of periodic orbits of period three prevents the existence of transitivity.