Global attractors in the parametrized Hénon–Devaney map

Authors

  • Bladismir Leal Instituto de Ciencias Básicas, Universidad Técnica de Manabí, Av. José María Urbina, Portoviejo, Ecuador. Facultad de Ingeniería, Universidad Nacional de Chimborazo, Vía Guano km 1.5, Riobamba, Ecuador
  • Sergio Muñoz Faculdade de Tecnologia, Dpto. de Matemática, Física e Computa¸c˜ao, Universidade do Estado do Rio de Janeiro, Resende, Brasil

DOI:

https://doi.org/10.33044/revuma.2133

Abstract

Given two positive real numbers $a$ and $c$, we consider the (two-parameter) family of nonlinear mappings \[ F_{a,c}(x,y)=\left(ax+\frac{1}{y}, \, c y-\frac{c}{y}-a c x\right). \] $F_{1,1}$ is the classical Hénon–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.

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Author Biography

Bladismir Leal, Instituto de Ciencias Básicas, Universidad Técnica de Manabí, Av. José María Urbina, Portoviejo, Ecuador. Facultad de Ingeniería, Universidad Nacional de Chimborazo, Vía Guano km 1.5, Riobamba, Ecuador

Dpto de Matematicas Facultad de Ciencias. Agregado D.E.

References

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Published

2023-04-18

Issue

Vol. 65 No. 1 (2023)

Section

Article

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Copyright (c) 2023 Luis Bladismir Ruiz Leal, Sergio Muñoz

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