On the maximal invariant set for the map X² - 2 restricted to intervals

• Bednařík, Dušan ^[2] ; Marques, Diego ^[1] ; Moreira, Carlos Gustavo Tamm de Araujo ; Trojovský, Pavel ^[2]
  1. [1] Universidade de Brasília

     Universidade de Brasília

     Brasil

     
  2. [2] University of Hradec Králové
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 2, 2021, págs. 305-312
• Idioma: inglés
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• Resumen

  • In this paper, we study the maximal invariant set of a quadratic family related to a class of unimodal maps. This family is very important and have direct application in many branches of science. In particular, we characterize when the maximal invariant of f(x) = x2 − 2 (restricted to an interval) has a chaotic behavior.