Global attractors in the parametrized Hénon–Devaney map

• Bladismir Leal ^[1] ; Sergio Muñoz ^[2]
  1. [1] Universidad Técnica de Manabí

     Universidad Técnica de Manabí

     Portoviejo, Ecuador

     
  2. [2] Universidad Nacional de Chimborazo

     Universidad Nacional de Chimborazo

     Riobamba, Ecuador

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 65, Nº. 1, 2023, págs. 79-101
• Idioma: inglés
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• Resumen

  • Given two positive real numbers a and c, we consider the (twoparameter) family of nonlinear mappings Fa,c(x, y) = ax +1 y , cy −cy− acx.

    F1,1 is the classical H´enon–Devaney map. For a large region of parameters, we exhibit an invariant non-bounded closed set with fractal structure which is a global attractor. Our approach leads to an in-depth understanding of the Hénon–Devaney map and its perturbations.