Global attractors in the parametrized Hénon–Devaney map

Abstract

Given two positive real numbers a and c, we consider the (twoparameter) family of nonlinear mappingsF 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.