Revista de la
Unión Matemática Argentina
Global attractors in the parametrized Hénon–Devaney map
Bladismir Leal and Sergio Muñoz
Volume 65, no. 1 (2023), pp. 79–101    

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

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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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